WBPSC Clerkship Mathematics Previous Year Questions with Answers

Correct Answer: (C) 6 2/3 days

Explanation

Work done by 10 men in 1 day = 1/15

Work done by 15 women in 1 day = 1/12

Work done by all together in 1 day = 1/15 + 1/12

= 4/60 + 5/60

= 9/60

= 3/20

Time taken = 1 ÷ (3/20)

= 20/3 days

= 6 2/3 days

Hence, the work will be completed in 6 2/3 days.

Shortcut Method

Time together = (a × b)/(a + b)

= (15 × 12)/(15 + 12)

= 180/27

= 6 2/3 days

Answer: (C) 6 2/3 days

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Correct Answer: (D) 87.5 km/hr

Explanation

Distance covered by second train = 400 km

Time taken = 4 hrs

Speed of second train = Distance/Time

= 400/4

= 100 km/hr

Ratio of speeds = 7 : 8

8 parts = 100 km/hr

1 part = 100/8 = 12.5 km/hr

Speed of first train = 7 parts

= 7 × 12.5

= 87.5 km/hr

Hence, the speed of the first train is 87.5 km/hr.

Shortcut Method

Speed of first train = Speed of second train × 7/8

= 100 × 7/8

= 87.5 km/hr

Answer: (D) 87.5 km/hr

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Correct Answer: (D) 5 and 7

Explanation

Number = 143, Remainder = 3

Required divisor divides (143 − 3) exactly

143 − 3 = 140

140 = 2 × 2 × 5 × 7

Prime factors of 140 = 2, 5, 7

Divisor must be greater than the remainder 3, so 2 is rejected

Check: 143 = 5 × 28 + 3

Check: 143 = 7 × 20 + 3

Hence, the required prime numbers are 5 and 7.

Shortcut Method

Divisor divides (N − R) and is greater than R

143 − 3 = 140 = 2^2 × 5 × 7

Primes greater than 3 = 5 and 7

Answer: (D) 5 and 7

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Correct Answer: (A) 64

Explanation

Remainder in each case = 12

1356 − 12 = 1344

1868 − 12 = 1856

2764 − 12 = 2752

Required number = HCF of 1344, 1856 and 2752

1344 = 64 × 21

1856 = 64 × 29

2752 = 64 × 43

21, 29 and 43 have no common factor

HCF = 64

Hence, the greatest number is 64.

Shortcut Method

Required number = HCF (a − r, b − r, c − r)

Check options on 1344: 1344 ÷ 64 = 21 (exact)

1344 ÷ 124, 1344 ÷ 156 and 1344 ÷ 260 are not exact

= 64

Answer: (A) 64

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Correct Answer: (C) 49 1/11 min. past 9

Explanation

At 9 o’clock, hour hand is 45 minute-spaces ahead of 12

Minute hand is at 12

Gap between the hands = 45 minute-spaces

Minute hand gains 55 minute-spaces in 60 minutes

Time to gain 45 minute-spaces = (60/55) × 45 min

= (12/11) × 45

= 540/11 min

= 49 1/11 min

Hence, the hands will be together at 49 1/11 min past 9.

Shortcut Method

Hands together between H and (H + 1) o’clock = (60/11) × H min past H

= (60/11) × 9

= 540/11

= 49 1/11 min past 9

Answer: (C) 49 1/11 min. past 9

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Correct Answer: (B) 8 1/3%

Explanation

Let Principal = P

Amount = 2P

SI = 2P − P = P

Time (T) = 12 years

SI = (P × R × T)/100

P = (P × R × 12)/100

R = 100/12

= 25/3

= 8 1/3%

Hence, the rate of interest is 8 1/3% per annum.

Shortcut Method

Sum becomes n times: R × T = 100 × (n − 1)

R × 12 = 100 × (2 − 1)

R = 100/12

= 8 1/3%

Answer: (B) 8 1/3%

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Correct Answer: (C) 4 1/2 hrs

Explanation

Speed in first 2 hrs = 70 km/hr

Distance in first 2 hrs = 70 × 2 = 140 km

Speed in next 2 hrs = 80 km/hr

Distance in next 2 hrs = 80 × 2 = 160 km

Distance in 4 hrs = 140 + 160 = 300 km

Remaining distance = 345 − 300 = 45 km

Speed after 4 hrs = 90 km/hr

Time for 45 km = 45/90 = 1/2 hr

Total time = 4 + 1/2

= 4 1/2 hrs

Hence, the car will cover 345 km in 4 1/2 hrs.

Shortcut Method

Check option (C) 4 1/2 hrs:

Distance = 70 × 2 + 80 × 2 + 90 × 1/2

= 140 + 160 + 45

= 345 km

Answer: (C) 4 1/2 hrs

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Correct Answer: (C) 23/30

Explanation

Girls = 3/5 of total

Boys = 1 − 3/5 = 2/5 of total

Absent girls = 2/9 × 3/5 = 2/15 of total

Absent boys = 1/4 × 2/5 = 1/10 of total

Total absent = 2/15 + 1/10

= 4/30 + 3/30

= 7/30

Present = 1 − 7/30

= 23/30

Hence, 23/30 of the total students are present.

Shortcut Method

Let total students = 90, so Girls = 54, Boys = 36

Absent = 2/9 × 54 + 1/4 × 36 = 12 + 9 = 21

Present = 90 − 21 = 69

= 69/90 = 23/30

Answer: (C) 23/30

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Correct Answer: (D) 60

Explanation

HCF = 8

Let the numbers be 8a and 8b (a and b co-prime)

LCM = 8 × a × b

So, LCM must be a multiple of 8

24 ÷ 8 = 3 (exact)

48 ÷ 8 = 6 (exact)

56 ÷ 8 = 7 (exact)

60 ÷ 8 = 7.5 (not exact)

Hence, 60 can never be the LCM.

Shortcut Method

HCF always divides LCM exactly

Only 60 is not divisible by 8

= 60

Answer: (D) 60

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Correct Answer: (B) 4000

Explanation

Let original number of eggs = x

Broken = 5%, so remaining = 95% of x

Sold = 93% of remainder, so left = 7% of remainder

7% of 95% of x = 266

(7/100) × (95/100) × x = 266

x = 266 × 100 × 100/(7 × 95)

= 2660000/665

= 4000

Hence, the shopkeeper originally had 4000 eggs.

Shortcut Method

Work backwards:

Remainder = 266 × 100/7 = 3800

Original = 3800 × 100/95

= 4000

Answer: (B) 4000

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Correct Answer: (A) 1

Explanation

Let the number = x

Condition: x + 1000 > 1000x

1000 > 1000x − x

1000 > 999x

x < 1000/999

x < 1.001 (approx.)

Only option (A) 1 is less than 1.001

Check: 1 + 1000 = 1001 and 1 × 1000 = 1000, and 1001 > 1000

Hence, the positive number is 1.

Shortcut Method

Check options:

x = 3: 1003 < 3000 (fails), and 5 and 7 also fail

x = 1: 1001 > 1000

= 1

Answer: (A) 1

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Correct Answer: (D) ₹ 325

Explanation

Let C’s share = ₹x

D’s share = ₹x

B’s share = ₹(x + 125)

A’s share = B + C = (x + 125) + x = ₹(2x + 125)

A + B + C + D = 750

(2x + 125) + (x + 125) + x + x = 750

5x + 250 = 750

5x = 500

x = 100

A’s share = 2 × 100 + 125

= ₹325

Hence, A’s share is ₹325.

Shortcut Method

A = B + C and D = C, so Total = 2A + C = 750

Try A = 325: C = 750 − 650 = 100

B = 325 − 100 = 225, and B − C = 125 (matches)

= ₹325

Answer: (D) ₹ 325

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Correct Answer: (C) 3 km/hr

Explanation

Speed of boat in still water = 10 km/hr

Let speed of stream = s km/hr

Downstream speed = (10 + s) km/hr

Upstream speed = (10 − s) km/hr

Time downstream = Time upstream

26/(10 + s) = 14/(10 − s)

26(10 − s) = 14(10 + s)

260 − 26s = 140 + 14s

40s = 120

s = 3

Hence, the speed of the stream is 3 km/hr.

Shortcut Method

Same time, so speed ratio = distance ratio = 26 : 14 = 13 : 7

13 + 7 = 20 = 2 × 10, so Downstream = 13, Upstream = 7

Stream speed = (Downstream − Upstream)/2

= (13 − 7)/2

= 3 km/hr

Answer: (C) 3 km/hr

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Correct Answer: (B) 75

Explanation

Soldiers : Captains = 15 : 1

Persons in one group = 15 + 1 = 16

Total persons = 1200

Number of groups = 1200/16

= 75

Each group has 1 captain

Number of captains = 75 × 1

= 75

Hence, the number of captains is 75.

Shortcut Method

Captains = 1/(15 + 1) × 1200

= 1200/16

= 75

Answer: (B) 75

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Correct Answer: (B) ₹ 30,000

Explanation

Let 1/2 of daughter’s share = 1/4 of wife’s share = 1/5 of son’s share = k

Daughter’s share = 2k

Wife’s share = 4k

Son’s share = 5k

2k + 4k + 5k = 1,65,000

11k = 1,65,000

k = 15,000

Daughter’s share = 2 × 15,000

= ₹30,000

Hence, the daughter’s share is ₹30,000.

Shortcut Method

Shares are in the ratio of the denominators = 2 : 4 : 5

Daughter’s share = 2/11 × 1,65,000

= ₹30,000

Answer: (B) ₹ 30,000

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Correct Answer: (D) 80%

Explanation

Total mixture = 60 gm

Water = 75% of 60 = (75/100) × 60 = 45 gm

Milk = 60 − 45 = 15 gm

Water added = 15 gm

New water = 45 + 15 = 60 gm

New mixture = 60 + 15 = 75 gm

Water % = (60/75) × 100

= 80%

Hence, the percentage of water is 80%.

Shortcut Method

Milk does not change = 15 gm

Milk % in new mixture = (15/75) × 100 = 20%

Water % = 100 − 20

= 80%

Answer: (D) 80%

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Correct Answer: (C) 60 km/hr

Explanation

Number of posts counted = 21

Number of gaps = 21 − 1 = 20

Distance between two posts = 50 m

Distance covered in 1 min = 20 × 50

= 1000 m

= 1 km

Speed = 1 km per minute

= 1 × 60 km/hr

= 60 km/hr

Hence, the train is travelling at 60 km/hr.

Shortcut Method

Distance = (n − 1) × gap = 20 × 50 = 1000 m per min

Speed (km/hr) = metres per min × 60/1000

= 1000 × 60/1000

= 60 km/hr

Answer: (C) 60 km/hr

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Correct Answer: (C) ₹ 900

Explanation

3 3/4 = 15/4

3 3/4 of ₹100 = (15/4) × 100

= ₹375

Let the sum = ₹x

5/12 of x = 375

x = 375 × 12/5

= 75 × 12

= ₹900

Hence, the required sum is ₹900.

Shortcut Method

5 parts (out of 12) = 375

1 part = 375/5 = 75

12 parts = 75 × 12

= ₹900

Answer: (C) ₹ 900

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Correct Answer: (B) ₹ 80

Explanation

Let CP = ₹x

Profit % = x%

Profit = x% of x = x^2/100

SP = CP + Profit

144 = x + x^2/100

14400 = 100x + x^2

x^2 + 100x − 14400 = 0

(x + 180)(x − 80) = 0

x = 80 (x = −180 is not possible)

Hence, the cost price of the article is ₹80.

Shortcut Method

SP = CP × (100 + Profit%)/100

Check option (B) ₹80:

= 80 × (100 + 80)/100

= 80 × 1.8

= ₹144

Answer: (B) ₹ 80

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Correct Answer: (B) ₹ 1,500

Explanation

Let total profit = ₹P

Charity = 5% of P

Profit left = 95% of P = 0.95P

A : B = 3 : 2

A’s share = 3/5 × 0.95P

= 0.57P

0.57P = 855

P = 855/0.57

= ₹1,500

Hence, the total profit is ₹1,500.

Shortcut Method

A’s share = 3/5 × 95/100 = 57/100 of total profit

Total profit = 855 × 100/57

= 15 × 100

= ₹1,500

Answer: (B) ₹ 1,500

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Correct Answer: (D) 84

Explanation

Number of values = 10

Average = 7

Sum = 10 × 7 = 70

Each number is multiplied by 12

New sum = 70 × 12 = 840

New average = 840/10

= 84

Hence, the new average is 84.

Shortcut Method

If each number is multiplied by k, the average is also multiplied by k

New average = 7 × 12

= 84

Answer: (D) 84

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Correct Answer: (A) 30 litres

Explanation

Let capacity = C litres

60% = 60/100 = 3/5 = 9/15

46 2/3% = (140/3)/100 = 7/15

Difference = 9/15 − 7/15

= 2/15

2/15 of C = 4 litres

C = 4 × 15/2

= 30 litres

Hence, the capacity of the bucket is 30 litres.

Shortcut Method

Difference = 60% − 46 2/3% = 13 1/3% = 2/15

Capacity = Difference in litres ÷ Difference in fraction

= 4 ÷ (2/15)

= 30 litres

Answer: (A) 30 litres

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Correct Answer: (C) 11 1/9

Explanation

First nine prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23

Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23

= 100

Number of terms = 9

Average = Sum/Number of terms

= 100/9

= 11 1/9

Hence, the average of the first nine prime numbers is 11 1/9.

Shortcut Method

Group the primes into round numbers:

Sum = (3 + 17) + (7 + 13) + (11 + 19) + (2 + 5 + 23)

= 20 + 20 + 30 + 30 = 100

Average = 100/9 = 11 1/9

Answer: (C) 11 1/9

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Correct Answer: (A) 8%

Explanation

List price = ₹1,500

First discount = 20% of 1500 = ₹300

Price after first discount = 1500 − 300 = ₹1,200

Net price required = ₹1,104

Additional discount = 1200 − 1104 = ₹96

Additional discount % = (96/1200) × 100

= 8%

Hence, the additional discount is 8%.

Shortcut Method

Net price = List price × (100 − d1)/100 × (100 − d2)/100

1104 = 1500 × 80/100 × (100 − d2)/100

(100 − d2)/100 = 1104/1200 = 0.92

d2 = 8%

Answer: (A) 8%

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Correct Answer: (B) 21 days

Explanation

Same work, so (2 men + 7 boys) × 14 = (3 men + 8 boys) × 11

28 men + 98 boys = 33 men + 88 boys

10 boys = 5 men

1 man = 2 boys

2 men + 7 boys = 4 + 7 = 11 boys

Total work = 11 × 14 = 154 boy-days

8 men + 6 boys = 16 + 6 = 22 boys

Three times the work = 3 × 154 = 462 boy-days

Days required = 462/22

= 21 days

Hence, 8 men and 6 boys can do three times the work in 21 days.

Shortcut Method

(M1 × D1)/W1 = (M2 × D2)/W2 (all in boys)

(11 × 14)/1 = (22 × D)/3

D = 11 × 14 × 3/22

= 21 days

Answer: (B) 21 days

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Correct Answer: (D) 3600

Explanation

LCM of 3, 4, 5, 6, 8 = 120

120 = 2 × 2 × 2 × 3 × 5

= 2^3 × 3 × 5

For a perfect square, each prime must have an even power

Multiply by 2 × 3 × 5 = 30

Required number = 120 × 30

= 3600

= 60^2

Hence, the least perfect square divisible by 3, 4, 5, 6 and 8 is 3600.

Shortcut Method

Check options:

900 ÷ 8 is not exact, 2500 ÷ 3 is not exact

1200 is not a perfect square

= 3600

Answer: (D) 3600

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Correct Answer: (B) 998996

Explanation

999 995/999 = 999 + 995/999

(999 + 995/999) × 999

= 999 × 999 + (995/999) × 999

= 999 × 999 + 995

999 × 999 = (1000 − 1)^2

= 1000000 − 2000 + 1

= 998001

Required value = 998001 + 995

= 998996

Hence, the value is 998996.

Shortcut Method

(a + b/a) × a = a^2 + b

= 999^2 + 995

= 998001 + 995

= 998996

Answer: (B) 998996

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Correct Answer: (B) 1/3

Explanation

1/4 of tank = 135 litres

Full tank = 135 × 4

= 540 litres

Water in tank = 180 litres

Part filled = 180/540

= 1/3

Hence, 1/3 of the tank is full.

Shortcut Method

Part filled = (180/135) × 1/4

= (4/3) × 1/4

= 1/3

Answer: (B) 1/3

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Correct Answer: (B) 30%

Explanation

Let the number = x

After 35% reduction = 65% of x

65% of x = 325

x = 325 × 100/65

= 500

Required increase = 650 − 500 = 150

Increase % = (150/500) × 100

= 30%

Hence, the number should be increased by 30% (taking the increase on the original number 500).

Shortcut Method

Original = 325 ÷ 0.65 = 500

New ÷ Original = 650/500 = 1.30

= 30% increase

Answer: (B) 30%

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Correct Answer: (D) 5

Explanation

January has 31 days = 4 weeks + 3 days, so the first 3 weekdays of the month occur 5 times. If 1 January is Monday, the extra days are Monday, Tuesday and Wednesday, so the Wednesdays fall on 3, 10, 17, 24 and 31 January, which is 5.

Exam Facts

• Rule: a 31-day month has 3 odd days, so the first three weekdays of the month occur 5 times and the rest 4 times.
• A 30-day month has 2 odd days, so the first two weekdays occur 5 times.
• February in a non-leap year (28 days) has every weekday exactly 4 times.
• Check: Wednesdays are 3, 10, 17, 24, 31, which is 5 dates within 31.
• 6 (option A) is impossible, since no month has more than 5 of any weekday.
• 4 (option B) applies to Thursday to Sunday in this January.
• 3 (option C) can never happen in any month.
• In this January, Monday, Tuesday and Wednesday occur 5 times each.
• Odd days concept: number of days beyond complete weeks (days mod 7).
• An ordinary year has 1 odd day and a leap year has 2 odd days.

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Correct Answer: (C) Causation

Explanation

When one event directly produces another, the relationship is causation (cause and effect). Correlation only means two things vary together, without proving that one causes the other.

Exam Facts

• Key rule: “Correlation does not imply causation.”
• Example of causation: heating water to 100°C at sea level causes it to boil.
• Correlation (option A) is a statistical link measured by the correlation coefficient (r), from −1 to +1.
• Comparison (option B) is examining similarities and differences.
• Association (option D) is a general relationship between variables, not necessarily causal.
• Example of correlation without causation: ice-cream sales and drowning both rise in summer.
• The confusing third factor in such cases is a confounding variable.
• Causation is proved through controlled experiments.
• In reasoning tests, cause and effect questions ask which statement is the cause.
• Karl Pearson developed the correlation coefficient.

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Correct Answer: (C) 120 gallons

Explanation

Time taken by first pipe = 20 minutes

Time taken by second pipe = 24 minutes

Time taken by all three pipes together = 15 minutes

Part filled by first pipe in 1 minute = 1/20

Part filled by second pipe in 1 minute = 1/24

Part filled by all three in 1 minute = 1/15

Part emptied by waste pipe in 1 minute = (1/20 + 1/24) − 1/15

= 6/120 + 5/120 − 8/120

= 3/120

= 1/40

So the waste pipe empties the full tank in 40 minutes.

Waste pipe empties 3 gallons per minute

Capacity = 40 × 3

= 120 gallons

Hence, the capacity of the tank is 120 gallons.

Shortcut Method

Let tank = LCM of 20, 24, 15 = 120 units

First pipe = 120/20 = 6 units/min, Second pipe = 120/24 = 5 units/min

All three = 120/15 = 8 units/min

Waste pipe = 6 + 5 − 8 = 3 units/min = 3 gallons/min

So 1 unit = 1 gallon, Capacity = 120 gallons

Answer: (C) 120 gallons

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Correct Answer: (C) 12 km/hr

Explanation

Total distance = 6 km

Total time = 45 minutes

Distance covered first = 1/2 × 6 = 3 km

Time used = 2/3 × 45 = 30 minutes

Remaining distance = 6 − 3 = 3 km

Remaining time = 45 − 30 = 15 minutes

= 15/60 hr

= 1/4 hr

Speed = Distance ÷ Time

= 3 ÷ (1/4)

= 3 × 4

= 12 km/hr

Hence, his speed must be 12 km/hr.

Shortcut Method

Remaining time = 1/3 of 45 = 15 min, remaining distance = 3 km

15 min is 1/4 of an hour

Speed = 3 × 4

= 12 km/hr

Answer: (C) 12 km/hr

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Correct Answer: (B) 6 days

Explanation

A does 1/2 of the work in 5 days

Time taken by A for whole work = 5 × 2 = 10 days

B does 2/5 of the work in 6 days

Time taken by B for whole work = 6 × 5/2 = 15 days

Work done by A in 1 day = 1/10

Work done by B in 1 day = 1/15

Work done by (A + B) in 1 day = 1/10 + 1/15

= 3/30 + 2/30

= 5/30

= 1/6

Time taken together = 1 ÷ (1/6)

= 6 days

Hence, A and B together will complete the work in 6 days.

Shortcut Method

Time together = (a × b)/(a + b)

= (10 × 15)/(10 + 15)

= 150/25

= 6 days

Answer: (B) 6 days

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Correct Answer: (B) 89 sec.

Explanation

Length of train = 240 m

Time to pass a pole = 24 sec

Speed = Distance ÷ Time

= 240 ÷ 24

= 10 m/sec

Distance to pass a platform = Length of train + Length of platform

= 240 + 650

= 890 m

Time = Distance ÷ Speed

= 890 ÷ 10

= 89 sec

Hence, the train will take 89 seconds to pass the platform.

Shortcut Method

Time = (Train + Platform)/Speed

= (240 + 650)/10

= 89 sec

Answer: (B) 89 sec.

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Correct Answer: (B) 2 : 1

Explanation

Let man’s age = 7x years

Son’s age = 3x years

Product of ages = 7x × 3x = 756

21x^2 = 756

x^2 = 756 ÷ 21

= 36

x = 6

Man’s age = 7 × 6 = 42 years

Son’s age = 3 × 6 = 18 years

After 6 years, man’s age = 42 + 6 = 48 years

After 6 years, son’s age = 18 + 6 = 24 years

Ratio = 48 : 24

= 2 : 1

Hence, the ratio of their ages after 6 years will be 2 : 1.

Shortcut Method

x^2 = Product ÷ (7 × 3) = 756 ÷ 21 = 36, so x = 6

New ratio = (7x + 6) : (3x + 6)

= 48 : 24

= 2 : 1

Answer: (B) 2 : 1

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Correct Answer: (D) 3.6 km

Explanation

Speed of boat in still water (B) = 15 km/hr

Speed of current (S) = 3 km/hr

Downstream speed = B + S

= 15 + 3

= 18 km/hr

Time = 12 minutes

= 12/60 hr

= 1/5 hr

Distance = Speed × Time

= 18 × 1/5

= 3.6 km

Hence, the distance travelled downstream in 12 minutes is 3.6 km.

Shortcut Method

Downstream speed = 18 km/hr = 18 km in 60 minutes

12 minutes = 1/5 of an hour

Distance = 18 ÷ 5

= 3.6 km

Answer: (D) 3.6 km

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Correct Answer: (B) 5%

Explanation

Principal (P) = Rs. 500

Simple Interest (SI) = Rs. 100

Time (T) = 4 years

Rate (R) = (SI × 100)/(P × T)

= (100 × 100)/(500 × 4)

= 10000/2000

= 5%

Hence, the rate of interest is 5% per annum.

Shortcut Method

Interest for 1 year = 100 ÷ 4 = Rs. 25

Rate = (25/500) × 100

= 5%

Answer: (B) 5%

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Correct Answer: (D) 10080

Explanation

Required number must be a multiple of LCM of 12, 15 and 18

12 = 2^2 × 3

15 = 3 × 5

18 = 2 × 3^2

LCM = 2^2 × 3^2 × 5

= 180

Smallest five-digit number = 10000

10000 ÷ 180 = 55, remainder 100

Required number = 10000 + (180 − 100)

= 10000 + 80

= 10080

Check: 10080 ÷ 180 = 56 exactly

Hence, the least five-digit number exactly divisible by 12, 15 and 18 is 10080.

Shortcut Method

A multiple of 180 must be divisible by 20 and by 9

Last two digits divisible by 20: only 10020 and 10080 qualify

Digit sum divisible by 9: 1 + 0 + 0 + 2 + 0 = 3 (no), 1 + 0 + 0 + 8 + 0 = 9 (yes)

= 10080

Answer: (D) 10080

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Correct Answer: (C) 30 days

Explanation

Efficiency of A : B = 3 : 1

Time taken by A : B = 1 : 3

Let time taken by A = x days

Time taken by B = 3x days

Difference in time = 3x − x = 80 days

2x = 80

x = 40

Time taken by A = 40 days

Time taken by B = 3 × 40 = 120 days

Work done by (A + B) in 1 day = 1/40 + 1/120

= 3/120 + 1/120

= 4/120

= 1/30

Time taken together = 30 days

Hence, working together they will complete the work in 30 days.

Shortcut Method

Time ratio 1 : 3, difference = 2 parts = 80 days, so 1 part = 40 days

A = 40 days, B = 120 days

Together = (40 × 120)/(40 + 120)

= 4800/160

= 30 days

Answer: (C) 30 days

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Correct Answer: (D) ₹ 67,500

Explanation

A’s capital = Rs. 30,000 for 12 months

B joins after 4 months, so B’s time = 12 − 4 = 8 months

Let B’s capital = Rs. x

Profit ratio = (Capital × Time) ratio

A : B = (30,000 × 12) : (x × 8)

= 3,60,000 : 8x

Given A : B = 2 : 3

3,60,000/8x = 2/3

16x = 3 × 3,60,000

16x = 10,80,000

x = 10,80,000/16

= Rs. 67,500

Hence, B’s contribution in the capital is Rs. 67,500.

Shortcut Method

B’s capital = A’s capital × (B’s share/A’s share) × (A’s time/B’s time)

= 30,000 × (3/2) × (12/8)

= 30,000 × 9/4

= Rs. 67,500

Answer: (D) ₹ 67,500

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Correct Answer: (A) 10%

Explanation

Let SP of 1 orange = Rs. 1

SP of 36 oranges = Rs. 36

Loss = SP of 4 oranges = Rs. 4

CP of 36 oranges = SP + Loss

= 36 + 4

= Rs. 40

Loss % = (Loss/CP) × 100

= (4/40) × 100

= 10%

Hence, his loss percent is 10%.

Shortcut Method

When loss = SP of x articles on selling n articles:

Loss % = x/(n + x) × 100

= 4/(36 + 4) × 100

= 10%

Answer: (A) 10%

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Correct Answer: (C) 17 1/7 mins past 10 a.m.

Explanation

Let the distance between Howrah and Burdwan = D km

Train 1 takes 8 a.m. to 12 noon = 4 hours

Speed of Train 1 = D/4 km/hr

Train 2 takes 9 a.m. to 12 noon = 3 hours

Speed of Train 2 = D/3 km/hr

Distance covered by Train 1 from 8 a.m. to 9 a.m. = D/4

Distance left at 9 a.m. = D − D/4 = 3D/4

Relative speed (opposite directions) = D/4 + D/3

= 3D/12 + 4D/12

= 7D/12 km/hr

Time to meet after 9 a.m. = (3D/4) ÷ (7D/12)

= (3/4) × (12/7)

= 9/7 hours

= 1 2/7 hours

= 1 hour + (2/7 × 60) minutes

= 1 hour 17 1/7 minutes

Meeting time = 9 a.m. + 1 hour 17 1/7 minutes

= 10:17 1/7 a.m.

Hence, the trains meet at 17 1/7 minutes past 10 a.m.

Shortcut Method

Take D = LCM of 4 and 3 = 12 units

Speeds = 12/4 = 3 units/hr and 12/3 = 4 units/hr

At 9 a.m. distance left = 12 − 3 = 9 units

Time = 9 ÷ (3 + 4) = 9/7 hr = 1 hr 17 1/7 min

= 17 1/7 mins past 10 a.m.

Answer: (C) 17 1/7 mins past 10 a.m.

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Correct Answer: (A) 125 cm

Explanation

Height at the end of the year = 133 cm

Increase during the year = 6.4%

Let height at the beginning = x cm

Height at the end = x × (100 + 6.4)/100

x × 106.4/100 = 133

x = 133 × 100/106.4

= 13300/106.4

= 125 cm

Hence, his height at the beginning of the year was 125 cm.

Shortcut Method

Original value = Final value × 100/(100 + Increase %)

= 133 × 100/106.4

= 125 cm

Check: 125 × 1.064 = 133 cm

Answer: (A) 125 cm

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Correct Answer: (B) 8,560

Explanation

Copies sold last week = 8,000

Increase this week = 7%

Increase = (7/100) × 8,000

= 560 copies

Copies sold this week = 8,000 + 560

= 8,560

Hence, 8,560 copies were sold this week.

Shortcut Method

New value = Old value × (100 + 7)/100

= 8,000 × 1.07

= 8,560

Answer: (B) 8,560

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Correct Answer: (B) ₹ 1,804

Explanation

SP = Rs. 2,050

Gain = 25%

CP = SP × 100/(100 + Gain %)

= 2,050 × 100/125

= Rs. 1,640

New profit = 10%

New SP = CP × (100 + 10)/100

= 1,640 × 110/100

= Rs. 1,804

Hence, the selling price will be Rs. 1,804.

Shortcut Method

New SP = Old SP × (100 + new gain %)/(100 + old gain %)

= 2,050 × 110/125

= 2,050 × 0.88

= Rs. 1,804

Answer: (B) ₹ 1,804

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Correct Answer: (B) 11/12

Explanation

Write each term as 1/(n × (n + 1))

1/2 = 1/(1 × 2), 1/6 = 1/(2 × 3), 1/12 = 1/(3 × 4), … , 1/132 = 1/(11 × 12)

Formula: 1/(n × (n + 1)) = 1/n − 1/(n + 1)

Sum = (1 − 1/2) + (1/2 − 1/3) + (1/3 − 1/4) + … + (1/11 − 1/12)

All middle terms cancel out

Sum = 1 − 1/12

= 11/12

Hence, the sum is 11/12.

Shortcut Method

Sum of 1/(n(n + 1)) from n = 1 to n = k is k/(k + 1)

Here there are 11 terms, so k = 11

= 11/(11 + 1)

= 11/12

Answer: (B) 11/12

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Correct Answer: (C) 44

Explanation

Let average after 20 innings = x

Total runs in 20 innings = 20x

Runs in 21st innings = 84

New average after 21 innings = x + 2

Total runs in 21 innings = 21 × (x + 2)

20x + 84 = 21x + 42

x = 84 − 42

= 42

Average after 21st innings = 42 + 2

= 44

Hence, his average after the 21st innings is 44 runs.

Shortcut Method

New average = Runs in last innings − (Previous innings × Increase)

= 84 − (20 × 2)

= 84 − 40

= 44

Answer: (C) 44

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Correct Answer: (C) 280

Explanation

Number of males = 160

Each male gets Rs. 4

Total share of males = 160 × 4

= Rs. 640

Males’ share : Females’ share = 16 : 21

16 parts = Rs. 640

1 part = 640/16 = Rs. 40

Females’ share = 21 × 40

= Rs. 840

Each female gets Rs. 3

Number of females = 840/3

= 280

Hence, the number of females is 280.

Shortcut Method

Females’ share = Males’ share × 21/16

= 640 × 21/16 = Rs. 840

Number of females = 840 ÷ 3

= 280

Answer: (C) 280

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Correct Answer: (A) 1 : 1

Explanation

Let the first number = a and the second number = b

60% of a = 3/5 of b

(60/100) × a = (3/5) × b

(3/5) × a = (3/5) × b

a = b

a : b = 1 : 1

Hence, the ratio of the first number to the second number is 1 : 1.

Shortcut Method

60% = 60/100 = 3/5

Both numbers are multiplied by the same fraction 3/5

So the numbers are equal

= 1 : 1

Answer: (A) 1 : 1

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Correct Answer: (A) ₹ 1,677

Explanation

Profit when sold at Rs. 1,864 = Loss when sold at Rs. 1,490

Let CP = Rs. x

Profit = SP − CP = 1,864 − x

Loss = CP − SP = x − 1,490

1,864 − x = x − 1,490

2x = 1,864 + 1,490

2x = 3,354

x = 3,354/2

= Rs. 1,677

Hence, the cost price of the article is Rs. 1,677.

Shortcut Method

When profit at SP1 = loss at SP2:

CP = (SP1 + SP2)/2

= (1,864 + 1,490)/2

= Rs. 1,677

Answer: (A) ₹ 1,677

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Correct Answer: (A) 5

Explanation

Total outcomes when two dice are thrown = 6 × 6 = 36

Required sum = 8

Favourable pairs (first die, second die):

= (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)

Number of pairs = 5

(1, 7) is not possible because a die shows at most 6

Hence, there are 5 different possibilities.

Shortcut Method

Ways to get sum S with two dice = S − 1 (for S = 2 to 7) or 13 − S (for S = 7 to 12)

Sum = 8, so ways = 13 − 8

= 5

Answer: (A) 5

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Correct Answer: (A) 65, 91

Explanation

HCF = 13

Ratio of the numbers = 5 : 7

Let the numbers be 5x and 7x

Since 5 and 7 are co-prime, HCF of 5x and 7x = x

x = 13

First number = 5 × 13 = 65

Second number = 7 × 13 = 91

Hence, the numbers are 65 and 91.

Shortcut Method

Numbers = HCF × each term of the ratio

= 13 × 5 and 13 × 7

= 65 and 91

Check: only option (A) has both numbers divisible by 13

Answer: (A) 65, 91

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Correct Answer: (A) 13.5 sec.

Explanation

Speed = 80 km/hr

= 80 × 5/18 m/s

= 200/9 m/s

Time to cross a tree = 4.5 s

Length of train = Speed × Time

= 200/9 × 4.5

= 100 m

Distance to cross the station = Length of train + Length of station

= 100 + 200

= 300 m

Time = Distance ÷ Speed

= 300 ÷ (200/9)

= 300 × 9/200

= 13.5 s

Hence, the train takes 13.5 seconds to cross the station.

Shortcut Method

At the same speed, time is proportional to distance

Train covers 100 m (its own length) in 4.5 s

Extra 200 m takes 4.5 × 200/100 = 9 s

Total time = 4.5 + 9

= 13.5 s

Answer: (A) 13.5 sec.

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Correct Answer: (C) 312

Explanation

Digits = 0, 2, 4 (each used once)

Largest 3-digit number = 420 (digits in descending order)

Smallest 3-digit number = 204 (0 cannot be in the hundreds place)

Average = (420 + 204)/2

= 624/2

= 312

Hence, the average of the largest and the smallest number is 312.

Shortcut Method

Average place by place (no carrying needed here):

Hundreds = (4 + 2)/2 = 3

Tens = (2 + 0)/2 = 1

Units = (0 + 4)/2 = 2

= 312

Answer: (C) 312

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Correct Answer: (B) 3

Explanation

Let the number be x

Given: x + 1 1/2 = x × 1 1/2

x + 3/2 = 3x/2

3x/2 − x = 3/2

x/2 = 3/2

x = 3

Check: 3 + 1.5 = 4.5 and 3 × 1.5 = 4.5

Hence, the required number is 3.

Shortcut Method

If x + a = x × a, then x = a/(a − 1)

= (3/2) ÷ (3/2 − 1)

= (3/2) ÷ (1/2)

= 3

Answer: (B) 3

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Correct Answer: (C) 2/5

Explanation

Total students = 40

Rice only = 1/5 of 40 = 8

Chapatti only = 2/5 of 40 = 16

Both = 40 − (8 + 16)

= 40 − 24

= 16

Fraction who like both = 16/40

= 2/5

Hence, 2/5 of the students like to eat both.

Shortcut Method

Fraction for both = 1 − (1/5 + 2/5)

= 1 − 3/5

= 2/5

Answer: (C) 2/5

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Correct Answer: (B) 6.216

Explanation

∛175616 = 56

175.616 = 175616/10^3, so ∛175.616 = 56/10 = 5.6

0.175616 = 175616/10^6, so ∛0.175616 = 56/100 = 0.56

0.000175616 = 175616/10^9, so ∛0.000175616 = 56/1000 = 0.056

Sum = 5.6 + 0.56 + 0.056

= 6.216

Hence, the value is 6.216.

Shortcut Method

Every 3 decimal places in the number give 1 decimal place in the cube root

3, 6 and 9 decimal places give 1, 2 and 3 places

= 5.6 + 0.56 + 0.056

= 6.216

Answer: (B) 6.216

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Correct Answer: (B) 5:50

Explanation

Ruma’s speed = 30 pages/hr

Neera’s speed = 40 pages/hr

Time gap = 3:20 − 2:30 = 50 min = 5/6 hr

Pages read by Ruma in 50 min = 30 × 5/6 = 25 pages

Relative speed = 40 − 30 = 10 pages/hr

Time for Neera to catch up = 25 ÷ 10

= 2.5 hr

= 2 hr 30 min

Meeting time = 3:20 + 2 hr 30 min

= 5:50

Check: by 5:50 Ruma reads 30 × 10/3 = 100 pages and Neera reads 40 × 5/2 = 100 pages

Hence, they will be reading the same page at 5:50.

Shortcut Method

Catch-up time = Lead ÷ Relative speed

= (30 × 50/60) ÷ (40 − 30)

= 25 ÷ 10 = 2.5 hr after 3:20

= 5:50

Answer: (B) 5:50

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Correct Answer: (A) 22 2/9%

Explanation

Let income = Rs. 100

Saving = 10% of 100 = Rs. 10

Expenditure = 100 − 10 = Rs. 90

New income = 100 + 20% of 100 = Rs. 120

New saving = Rs. 10 (same as before)

New expenditure = 120 − 10 = Rs. 110

Increase in expenditure = 110 − 90 = Rs. 20

Percentage increase = (20/90) × 100

= 200/9 %

= 22 2/9 %

Hence, his expenditure increased by 22 2/9%.

Shortcut Method

Saving is unchanged, so the whole rise in income goes into expenditure

% increase = (Rise in income/Old expenditure) × 100

= (20/90) × 100

= 22 2/9 %

Answer: (A) 22 2/9%

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Correct Answer: (D) 69

Explanation

The series follows ×2 + 1 and ×2 − 1 alternately: 4 × 2 + 1 = 9, 9 × 2 − 1 = 17, 17 × 2 + 1 = 35, so the next term is 35 × 2 − 1 = 69, and the check 69 × 2 + 1 = 139 confirms it. The missing number is 69.

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Correct Answer: (B) 2 : 3

Explanation

Let the first number = a and the second number = b

First number increased by 20% = a × 120/100 = 6a/5

Second number decreased by 20% = b × 80/100 = 4b/5

Given: 6a/5 = 4b/5

6a = 4b

a/b = 4/6

= 2/3

Hence, the ratio of the first and second number is 2 : 3.

Shortcut Method

a × 120 = b × 80

a : b = 80 : 120

= 2 : 3

Answer: (B) 2 : 3

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Correct Answer: (A) 31 : 9

Explanation

Total mixture = 40 litres, Milk : Water = 3 : 2

Milk = (3/5) × 40 = 24 litres

Water = (2/5) × 40 = 16 litres

Fraction of mixture removed each time = 10/40 = 1/4

Water left after 1st operation = 16 × (1 − 1/4)

= 16 × 3/4

= 12 litres

Water left after 2nd operation = 12 × 3/4

= 9 litres

Milk = 40 − 9 = 31 litres

Milk : Water = 31 : 9

Hence, the ratio of milk and water in the resulting mixture is 31 : 9.

Shortcut Method

Water left = Initial water × (1 − x/T)^n

= 16 × (1 − 10/40)^2

= 16 × 9/16

= 9 litres, so Milk : Water = (40 − 9) : 9 = 31 : 9

Answer: (A) 31 : 9

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Correct Answer: (A) 45 km/hr

Explanation

Let the length of the train = L metres and its speed = S m/s

Time to cross a man = 10 seconds, so L = S × 10

Time to cross the station = 22 seconds, so L + 150 = S × 22

Subtracting: (L + 150) − L = 22S − 10S

150 = 12S

S = 150/12

= 12.5 m/s

Speed in km/hr = 12.5 × 18/5

= 45 km/hr

Hence, the speed of the train is 45 km/hr.

Shortcut Method

Speed = Extra distance ÷ Extra time

= 150 ÷ (22 − 10)

= 12.5 m/s

= 12.5 × 18/5 = 45 km/hr

Answer: (A) 45 km/hr

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Correct Answer: (C) 96

Explanation

Let the number of students = n

Contribution of each student = Rs. n

Total amount = n × n = n^2

n^2 = 9216

9216 = 2^10 × 3^2

n = √9216 = 2^5 × 3

= 96

Hence, the number of students in the class is 96.

Shortcut Method

Unit digit of 9216 is 6, so √ ends in 4 or 6

92 lies between 9^2 = 81 and 10^2 = 100, so √ = 94 or 96

9 × 10 = 90 < 92, so take the larger: 96

Check: 96 × 96 = 9216

Answer: (C) 96

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Correct Answer: (B) 147

Explanation

Required number leaves remainder 3 when divided by 8, 12 and 16

8 = 2^3, 12 = 2^2 × 3, 16 = 2^4

LCM of 8, 12, 16 = 2^4 × 3

= 48

Required number = 48k + 3, which must be divisible by 7

k = 1: 48 + 3 = 51, 51 ÷ 7 leaves remainder 2

k = 2: 96 + 3 = 99, 99 ÷ 7 leaves remainder 1

k = 3: 144 + 3 = 147, 147 ÷ 7 = 21 exactly

Hence, the smallest such number is 147.

Shortcut Method

Option check: subtract the remainder 3 and test divisibility by LCM 48

140 − 3 = 137 (no), 147 − 3 = 144 = 48 × 3 (yes)

147 = 7 × 21, so 147 is divisible by 7

= 147

Answer: (B) 147

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Correct Answer: (A) ₹ 40

Explanation

A + B + C = Rs. 300

A + C = Rs. 188

B = (A + B + C) − (A + C)

= 300 − 188

= Rs. 112

B + C = Rs. 152

C = 152 − B

= 152 − 112

= Rs. 40

Hence, the daily earning of C is Rs. 40.

Shortcut Method

C = (A + C) + (B + C) − (A + B + C)

= 188 + 152 − 300

= Rs. 40

Answer: (A) ₹ 40

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Correct Answer: (A) 99000

Explanation

999 494/495 = 1000 − 1/495

999 494/495 × 99 = (1000 − 1/495) × 99

= 1000 × 99 − 99/495

= 99000 − 1/5

Value = 1/5 + 99000 − 1/5

= 99000

Hence, the value of the expression is 99000.

Shortcut Method

999 494/495 is just 1/495 less than 1000

1000 × 99 = 99000, and 99 × 1/495 = 1/5

The + 1/5 cancels the − 1/5

= 99000

Answer: (A) 99000

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Correct Answer: (C) 2 : 3

Explanation

Simple Interest (SI) = (P × R × T)/100

P and R are the same in both cases

SI for 6 years = (P × R × 6)/100

SI for 9 years = (P × R × 9)/100

Ratio = (P × R × 6)/100 : (P × R × 9)/100

= 6 : 9

= 2 : 3

Hence, the ratio of the simple interests is 2 : 3.

Shortcut Method

When P and R are fixed, SI ∝ T

SI(6 yrs) : SI(9 yrs) = 6 : 9

= 2 : 3

Answer: (C) 2 : 3

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Correct Answer: (D) ₹ 2,980

Explanation

Cost of 12 belts + 30 wallets = ₹ 8,940

4 belts + 10 wallets = (12 belts + 30 wallets) ÷ 3

Cost of 4 belts + 10 wallets = 8940 ÷ 3

= ₹ 2,980

Hence, the cost of 4 belts and 10 wallets is ₹ 2,980.

Shortcut Method

12 : 30 and 4 : 10 are both 2 : 5, and 4 = 12/3

Required cost = 8940 × (1/3)

= ₹ 2,980

Answer: (D) ₹ 2,980

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Correct Answer: (A) 20%

Explanation

Let B’s income = ₹ 100

A’s income = 100 + 25% of 100 = ₹ 125

Difference = 125 − 100 = ₹ 25

B’s income is less than A’s by = (Difference ÷ A’s income) × 100

= (25/125) × 100

= 20%

Hence, B’s income is 20% less than A’s income.

Shortcut Method

Required % = R/(100 + R) × 100

= 25/125 × 100

= 20%

Answer: (A) 20%

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Correct Answer: (D) ₹ 40

Explanation

Ratio of prices X : Z = 1 : 3

Let price of X = x and price of Z = 3x

Price of Y = Average of X and Z = ₹ 40

(x + 3x)/2 = 40

4x = 80

x = 20

Price of X = ₹ 20 and price of Z = 3 × 20 = ₹ 60

Difference = 60 − 20

= ₹ 40

Hence, the difference between the prices of Z and X is ₹ 40.

Shortcut Method

Sum of X and Z = 2 × 40 = ₹ 80

Difference = Sum × (3 − 1)/(3 + 1)

= 80 × 2/4

= ₹ 40

Answer: (D) ₹ 40

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Correct Answer: (B) 25.5%

Explanation

Ratio of boys : girls = 11 : 9

Let boys = 110 and girls = 90 (total = 200)

Boys passed = 30% of 110 = (30/100) × 110 = 33

Girls passed = 20% of 90 = (20/100) × 90 = 18

Total passed = 33 + 18 = 51

Pass percentage = (51/200) × 100

= 25.5%

Hence, 25.5% of the students of the class passed.

Shortcut Method

Weighted average = (11 × 30 + 9 × 20)/(11 + 9)

= (330 + 180)/20

= 510/20

= 25.5%

Answer: (B) 25.5%

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Correct Answer: (A) 8 days

Explanation

Y alone finishes the job in = 24 days

X works at double the speed of Y, so X takes half the time

X alone finishes the job in = 24 ÷ 2 = 12 days

X’s 1 day work = 1/12

Y’s 1 day work = 1/24

(X + Y)’s 1 day work = 1/12 + 1/24

= 2/24 + 1/24

= 3/24

= 1/8

Time taken together = 1 ÷ (1/8)

= 8 days

Hence, X and Y together can finish the job in 8 days.

Shortcut Method

Efficiency X : Y = 2 : 1, total work = 1 × 24 = 24 units

Time together = 24 ÷ (2 + 1)

= 8 days

Answer: (A) 8 days

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Correct Answer: (A) ₹ 1500

Explanation

Amal’s capital = ₹ 500 for 9 months

Let Bimal’s capital = ₹ x for 6 months

Total profit = ₹ 69, Bimal’s share = ₹ 46

Amal’s share = 69 − 46 = ₹ 23

Profit ratio = Capital × Time ratio

Amal : Bimal = (500 × 9) : (x × 6) = 23 : 46

4500/(6x) = 23/46 = 1/2

6x = 4500 × 2

6x = 9000

x = 1500

Hence, Bimal invested ₹ 1500.

Shortcut Method

Bimal’s share is 2 times Amal’s (46 = 2 × 23)

Bimal’s capital = 500 × 2 × (9/6)

= 500 × 3

= ₹ 1500

Answer: (A) ₹ 1500

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Correct Answer: (D) 131 kg

Explanation

Let the average weight of all 12 persons = a kg

Weight of the 12th person = (a + 33) kg

Total weight of first 11 persons = 11 × 95 = 1045 kg

Total weight of 12 persons = 12a

12a = 1045 + (a + 33)

12a − a = 1078

11a = 1078

a = 98 kg

Weight of the 12th person = 98 + 33

= 131 kg

Hence, the weight of the 12th person is 131 kg.

Shortcut Method

The 12th person’s extra 33 kg is shared by the other 11 persons

Increase in average = 33/11 = 3 kg, so a = 95 + 3 = 98 kg

12th person = 98 + 33

= 131 kg

Answer: (D) 131 kg

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Correct Answer: (A) 24 min.

Explanation

Time taken by pipe A = 60 min

Time taken by pipe B = 40 min

Part filled by A in 1 min = 1/60

Part filled by B in 1 min = 1/40

Part filled by (A + B) in 1 min = 1/60 + 1/40

= 2/120 + 3/120

= 5/120

= 1/24

Time taken together = 1 ÷ (1/24)

= 24 min

Hence, A and B together will fill the tanker in 24 minutes.

Shortcut Method

Time together = (a × b)/(a + b)

= (60 × 40)/(60 + 40)

= 2400/100

= 24 min

Answer: (A) 24 min.

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Correct Answer: (A) ₹ 4.50

Explanation

Amount spent = ₹ 6

Reduction in price = 12 1/2% = 1/8

Money saved = 12 1/2% of 6 = (1/8) × 6 = ₹ 0.75

With the money saved (₹ 0.75), 2 more oranges are bought

Reduced price of 1 orange = 0.75 ÷ 2 = ₹ 0.375

Reduced price of 1 dozen (12) oranges = 12 × 0.375

= ₹ 4.50

Hence, the reduced price of a dozen oranges is ₹ 4.50.

Shortcut Method

Reduced price per orange = (R% × Amount)/(100 × Extra quantity)

= (12.5 × 6)/(100 × 2)

= ₹ 0.375

Per dozen = 0.375 × 12 = ₹ 4.50

Answer: (A) ₹ 4.50

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Correct Answer: (B) 4 hours

Explanation

Speed of boat in still water = 8 km/hr

Speed of stream = 4 km/hr

Downstream speed = Boat speed + Stream speed

= 8 + 4

= 12 km/hr

Distance = 48 km

Time = Distance ÷ Speed

= 48 ÷ 12

= 4 hours

Hence, the boat takes 4 hours to go 48 km downstream.

Shortcut Method

Time downstream = D/(B + S)

= 48/(8 + 4)

= 4 hours

Answer: (B) 4 hours

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Correct Answer: (B) 133

Explanation

Let the two numbers be 3k and 4k (since quotient = 3/4)

Product = 3k × 4k = 4332

12k^2 = 4332

k^2 = 4332 ÷ 12

k^2 = 361

k = 19

First number = 3 × 19 = 57

Second number = 4 × 19 = 76

Sum = 57 + 76

= 133

Hence, the sum of the numbers is 133.

Shortcut Method

Sum = 7k (since 3k + 4k = 7k), so the sum must be a multiple of 7

Among the options, only 133 = 7 × 19 is a multiple of 7

Check: 57 × 76 = 4332

Answer: (B) 133

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Correct Answer: (C) 3600

Explanation

Number of boys must be divisible by 15, 18 and 24

15 = 3 × 5

18 = 2 × 3^2

24 = 2^3 × 3

LCM = 2^3 × 3^2 × 5 = 360

For a perfect square, every prime must have an even power

2^3 needs one more 2, and 5 needs one more 5

Least perfect square = 360 × 2 × 5

= 3600

Hence, the least number of boys in the school is 3600 (60 × 60).

Shortcut Method

Check options for divisibility by 360 (LCM)

4900 ÷ 360 and 2500 ÷ 360 are not whole numbers, 6400 ÷ 360 is not whole

3600 ÷ 360 = 10 and 3600 = 60^2

= 3600

Answer: (C) 3600

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Correct Answer: (D) 180 m

Explanation

Speed of slower train = 36 km/hr

Speed of faster train = 45 km/hr

Trains move in opposite directions

Relative speed = 36 + 45 = 81 km/hr

= 81 × 5/18 m/s

= 22.5 m/s

The man in the slower train sees the full length of the faster train pass in 8 seconds

Length of faster train = Relative speed × Time

= 22.5 × 8

= 180 m

Hence, the length of the faster train is 180 m.

Shortcut Method

Length = (S1 + S2) × 5/18 × t

= 81 × 5/18 × 8

= 180 m

Answer: (D) 180 m

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Correct Answer: (C) 435

Explanation

LCM = 2175, HCF = 145

One number = 725

Formula: First number × Second number = LCM × HCF

725 × Second number = 2175 × 145

Second number = (2175 × 145) ÷ 725

= 2175 ÷ 5

= 435

Hence, the other number is 435.

Shortcut Method

Other number = (LCM × HCF)/Given number

= 2175 × 145/725 = 2175/5

= 435

Check: 435 = 145 × 3, 725 = 145 × 5, LCM = 145 × 15 = 2175

Answer: (C) 435

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Correct Answer: (C) 28 students

Explanation

Total students = n(C ∪ B) = 45

Both games = n(C ∩ B) = 11

Only Chess = 17

Total in Chess = n(C) = 17 + 11 = 28

Formula: n(C ∪ B) = n(C) + n(B) − n(C ∩ B)

45 = 28 + n(B) − 11

45 = 17 + n(B)

n(B) = 45 − 17

= 28

Hence, 28 students participate in Badminton.

Shortcut Method

Everyone who is not “only Chess” plays Badminton

Badminton = Total − Only Chess

= 45 − 17

= 28 students

Answer: (C) 28 students

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Correct Answer: (B) 1 minute

Explanation

Length of goods train = 250 m

Length of mail train = 200 m

Speed of goods train = 33 km/hr

Speed of mail train = 60 km/hr

Both trains run in the same direction

Relative Speed = 60 − 33 = 27 km/hr

= 27 × 5/18 m/s

= 7.5 m/s

Distance to cover = 250 + 200 = 450 m

Time = Distance ÷ Relative Speed

= 450 ÷ 7.5

= 60 seconds

= 1 minute

Hence, the mail train takes 1 minute to cross the goods train.

Shortcut Method

Time (hr) = Total length (km) ÷ Relative speed (km/hr)

= 0.45 ÷ 27

= 1/60 hr

= 1 minute

Answer: (B) 1 minute

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Correct Answer: (B) 108 km/hr

Explanation

Length of bike = 2 m

Length of bridge = 22 m

Time = 0.8 sec

Distance covered = Length of bike + Length of bridge

= 2 + 22

= 24 m

Speed = Distance ÷ Time

= 24 ÷ 0.8

= 30 m/s

Speed in km/hr = 30 × 18/5

= 108 km/hr

Hence, the bike was travelling at 108 km/hr.

Shortcut Method

Speed (km/hr) = (Distance ÷ Time) × 3.6

= (24 ÷ 0.8) × 3.6

= 30 × 3.6

= 108 km/hr

Answer: (B) 108 km/hr

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Correct Answer: (A) 3 am

Explanation

Intervals of the bells = 45 min, 1 hr, 1 hr 15 min, 1 hr 30 min

In minutes = 45, 60, 75, 90

The bells ring together again after the LCM of the intervals

45 = 3^2 × 5

60 = 2^2 × 3 × 5

75 = 3 × 5^2

90 = 2 × 3^2 × 5

LCM = 2^2 × 3^2 × 5^2

= 4 × 9 × 25

= 900 minutes

= 900 ÷ 60 hours

= 15 hours

Time = 12 noon + 15 hours

= 3 am (next day)

Hence, the bells will ring together again at 3 am.

Shortcut Method

Take 15 minutes as 1 unit: 45, 60, 75, 90 min = 3, 4, 5, 6 units

LCM (3, 4, 5, 6) = 60 units

= 60 × 15 min = 900 min = 15 hours

12 noon + 15 hours = 3 am

Answer: (A) 3 am

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Correct Answer: (C) 20%

Explanation

Numbers from 1 to 70 = 70 numbers

Numbers with unit digit 1 = 1, 11, 21, 31, 41, 51, 61

= 7 numbers

Numbers with unit digit 9 = 9, 19, 29, 39, 49, 59, 69

= 7 numbers

Total = 7 + 7

= 14 numbers

Percentage = (14/70) × 100

= 20%

Hence, 20% of the numbers from 1 to 70 have 1 or 9 in the unit’s digit.

Shortcut Method

In every group of 10 numbers, 2 numbers end in 1 or 9

= 2/10 × 100

= 20%

Answer: (C) 20%

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Correct Answer: (A) 20

Explanation

Workers = 10

Time = 20 days

Total work = 10 × 20

= 200 worker-days

Work done in 10 days = 10 × 10

= 100 worker-days

Remaining work = 200 − 100

= 100 worker-days

Workers left = 50% of 10

= 5 workers

Days needed = 100 ÷ 5

= 20 days

Hence, 20 more days are needed to finish the job.

Shortcut Method

M1 × D1 = M2 × D2 (for the remaining work)

10 × (20 − 10) = 5 × D2

100 = 5 × D2

D2 = 20 days

Answer: (A) 20

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Correct Answer: (D) 80

Explanation

Let marks in English = E

Marks in Science = 2E

English : Mathematics = 2 : 3

Marks in Mathematics = 3E/2

Total = E + 2E + 3E/2 = 180

9E/2 = 180

E = 180 × 2/9

= 40

Marks in Science = 2 × 40

= 80

Hence, his marks in Science are 80.

Shortcut Method

English : Science : Mathematics = 2 : 4 : 3

Total parts = 2 + 4 + 3 = 9

1 part = 180 ÷ 9 = 20

Science = 4 × 20 = 80

Answer: (D) 80

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Correct Answer: (D) 326

Explanation

324 = 18², 441 = 21² and 289 = 17² are all perfect squares, but 326 lies between 18² = 324 and 19² = 361, so it is not a perfect square. Hence 326 is the odd one out.

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Correct Answer: (B) 3

Explanation

Prime factorisation of 5808:

5808 = 2 × 2904

= 2 × 2 × 1452

= 2 × 2 × 2 × 726

= 2 × 2 × 2 × 2 × 363

= 2^4 × 3 × 121

= 2^4 × 3 × 11^2

In a perfect square every prime factor must occur in pairs.

2^4 and 11^2 are already paired; only 3 is unpaired.

Required number = 3

Check: 5808 × 3 = 17424 = 132^2

Hence, the smallest number to multiply by is 3.

Shortcut Method

5808 = 16 × 363 = 16 × 3 × 121

16 = 4^2 and 121 = 11^2 are perfect squares

Left-over factor = 3

Answer: (B) 3

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Correct Answer: (B) ₹ 1,08,000

Explanation

Given: 2X = 3Y and Y = 4Z

From 2X = 3Y, X : Y = 3 : 2

From Y = 4Z, Y : Z = 4 : 1

Make Y equal in both ratios:

X : Y = 3 : 2 = 6 : 4

Y : Z = 4 : 1

X : Y : Z = 6 : 4 : 1

Sum of ratio terms = 6 + 4 + 1 = 11

Profit is shared in the ratio of capitals (same time period).

Share of Y = (4/11) × 2,97,000

= 4 × 27,000

= ₹ 1,08,000

Hence, the share of Y is ₹ 1,08,000.

Shortcut Method

Take Z = 1, then Y = 4 and X = 3Y/2 = 6

1 part = 2,97,000 ÷ 11 = 27,000

Y = 4 × 27,000 = ₹ 1,08,000

Answer: (B) ₹ 1,08,000

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Correct Answer: (A) 4 : 5

Explanation

Let the incomes of Simon and Anik be S and A.

Simon saves 25%, so Simon’s expenditure = 75% of S

Anik saves 40%, so Anik’s expenditure = 60% of A

Expenditures are equal:

(75/100) × S = (60/100) × A

75S = 60A

S/A = 60/75

= 4/5

S : A = 4 : 5

Hence, the ratio of the incomes of Simon and Anik is 4 : 5.

Shortcut Method

When expenditures are equal, income ratio = inverse of expenditure % ratio

S : A = 60 : 75

= 4 : 5

Answer: (A) 4 : 5

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Correct Answer: (D) 15 : 8 : 24

Explanation

Let 40% of P = 0.75 of Q = 1/4 of R = k

(40/100) × P = k, so P = k × 100/40 = 5k/2

0.75 × Q = k, so Q = k/0.75 = 4k/3

(1/4) × R = k, so R = 4k

P : Q : R = 5/2 : 4/3 : 4

LCM of denominators 2 and 3 = 6

Multiply each term by 6:

= 15 : 8 : 24

Hence, P : Q : R = 15 : 8 : 24.

Shortcut Method

40% = 2/5, 0.75 = 3/4, 1/4

P : Q : R = 5/2 : 4/3 : 4/1 = 15 : 8 : 24

Check with option D: 0.4 × 15 = 6, 0.75 × 8 = 6, 24/4 = 6 (all equal)

Answer: (D) 15 : 8 : 24

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Correct Answer: (B) ₹ 11,000

Explanation

Let the Cost Price (CP) = 100 units

Original SP at 10% gain = 110% of CP

New SP at 10% loss = 90% of CP

Fall in SP = 110% − 90% = 20% of CP

20% of CP = ₹ 2,000

CP = 2000 × (100/20)

= ₹ 10,000

Original SP = 110% of 10,000

= ₹ 11,000

Hence, the original selling price of the book-shelf is ₹ 11,000.

Shortcut Method

Gain% + Loss% = 10 + 10 = 20% of CP = ₹ 2,000

Original SP = 110% → (110/20) × 2,000

= ₹ 11,000

Answer: (B) ₹ 11,000

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Correct Answer: (C) might be even or might be odd.

Explanation

Let the books of the first student = n

Books of the 5 students = n, n + 2, n + 4, n + 6, n + 8

Total = 5n + (2 + 4 + 6 + 8)

= 5n + 20

20 is always even, so the result depends on 5n

If n is even, 5n is even, so Total = even + even = even

If n is odd, 5n is odd, so Total = odd + even = odd

Hence, the total number of books might be even or might be odd.

Shortcut Method

Try n = 1: 1 + 3 + 5 + 7 + 9 = 25 (odd)

Try n = 2: 2 + 4 + 6 + 8 + 10 = 30 (even)

The total can be either, so the answer is (C)

Answer: (C) might be even or might be odd.

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Correct Answer: (B) 12%

Explanation

Amount after 8 years = ₹ 12,005

Amount after 5 years = ₹ 9,800

SI for 3 years = 12005 − 9800 = ₹ 2,205

SI for 1 year = 2205 ÷ 3 = ₹ 735

SI for 5 years = 735 × 5 = ₹ 3,675

Principal (P) = 9800 − 3675 = ₹ 6,125

R = (SI × 100)/(P × T)

= (735 × 100)/(6125 × 1)

= 12%

Hence, the rate of interest is 12% per annum.

Shortcut Method

P = (A1 × T2 − A2 × T1)/(T2 − T1)

= (9800 × 8 − 12005 × 5)/(8 − 5)

= (78400 − 60025)/3 = ₹ 6,125

R = (735/6125) × 100 = 12%

Answer: (B) 12%

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Correct Answer: (A) All of them may be odd.

Explanation

Rules: Odd + Odd = Even, Even + Even = Even, Odd + Even = Odd

(A) x, y, z all odd: odd + odd + odd = even + odd = odd (not possible, sum must be even)

(B) x, y, z all even: even + even + even = even (possible)

(C) x, y odd and z even: odd + odd + even = even (possible)

(D) y, z odd and x even: even + odd + odd = even (possible)

Hence, the statement “All of them may be odd” is not correct.

Shortcut Method

A sum of three numbers is even only when the number of odd terms is 0 or 2

All three odd = 3 odd terms, so the sum is odd

Example: 1 + 3 + 5 = 9 (odd)

Answer: (A) All of them may be odd.

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Correct Answer: (A) 16 days

Explanation

The number of lotus doubles every day

The pond is half covered on day 15

On day 16, cover = 2 × (1/2)

= full pond

Hence, the entire pond will be covered in 16 days.

Shortcut Method

For doubling growth, full = half + 1 day

= 15 + 1

= 16 days

Answer: (A) 16 days

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Correct Answer: (D) 3 pm

Explanation

Distance XY = 465 km

Speed of train from X = 65 km/hr (starts at 10 am)

Distance covered by it till 11 am = 65 × 1 = 65 km

Remaining distance at 11 am = 465 − 65 = 400 km

Relative speed (opposite directions) = 65 + 35 = 100 km/hr

Time to meet = 400 ÷ 100 = 4 hours

Meeting time = 11 am + 4 hours = 3 pm

Hence, the two trains meet at 3 pm.

Shortcut Method

Let them meet t hours after 10 am

65t + 35(t − 1) = 465

100t = 500, so t = 5 hours

10 am + 5 hours = 3 pm

Answer: (D) 3 pm

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Correct Answer: (C) 12 km/hr

Explanation

Let the distance one way = D km

Time going = D/10 hr

Time returning = D/15 hr

Average speed = Total distance ÷ Total time

= 2D ÷ (D/10 + D/15)

= 2D ÷ (5D/30)

= 2D × 30/(5D)

= 12 km/hr

Hence, the average speed of the entire ride is 12 km/hr.

Shortcut Method

Average speed = 2xy/(x + y) (for equal distances)

= (2 × 10 × 15)/(10 + 15)

= 300/25

= 12 km/hr

Answer: (C) 12 km/hr

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Correct Answer: (B) 8

Explanation

Expression = 9 − 1 2/9 of 3 3/11 ÷ 5 1/7 of 7/9

Convert: 1 2/9 = 11/9, 3 3/11 = 36/11, 5 1/7 = 36/7

By BODMAS, “of” is done first

11/9 of 36/11 = (11/9) × (36/11) = 36/9 = 4

36/7 of 7/9 = (36/7) × (7/9) = 36/9 = 4

Division: 4 ÷ 4 = 1

Subtraction: 9 − 1 = 8

Hence, the value of the expression is 8.

Shortcut Method

Both “of” parts cancel to 36/9 = 4

= 9 − (4 ÷ 4)

= 9 − 1 = 8

Answer: (B) 8

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Correct Answer: (A) 2,53,000

Explanation

Present population (P) = 2,00,000

Increase in 1st year = 10%, in 2nd year = 15%

Population after 1 year = 200000 × 110/100 = 2,20,000

Population after 2 years = 220000 × 115/100

= 2,53,000

Hence, the population of the town after two years is 2,53,000.

Shortcut Method

Net % increase = a + b + (a × b)/100

= 10 + 15 + (10 × 15)/100 = 26.5%

Population = 200000 × 126.5/100 = 2,53,000

Answer: (A) 2,53,000

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Correct Answer: (B) [5×5×5]^2

Explanation

[(5+5)^2]^2 = (10^2)^2 = 100^2 = 10,000

[5×5×5]^2 = 125^2 = 15,625

[5+5+5]^3 = 15^3 = 3,375

[5^5+5^5+5^5+5^5] = 4 × 5^5

= 4 × 3125 = 12,500

Comparing: 15,625 > 12,500 > 10,000 > 3,375

Hence, the greatest number is [5×5×5]^2 = 15,625.

Shortcut Method

Write all as powers: 10^4, 5^6, 15^3, 4 × 5^5

5^6 = 5 × 5^5, which is more than 4 × 5^5

5^6 = 15625 is more than 10^4 = 10000, and 15^3 = 3375 is the smallest

So the greatest is (B)

Answer: (B) [5×5×5]^2

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Correct Answer: (D) 36 hours

Explanation

Tap A fills in 5 hours, so A’s 1 hour work = 1/5

Tap B fills in 20 hours, so B’s 1 hour work = 1/20

(A + B)’s 1 hour work = 1/5 + 1/20 = 5/20 = 1/4

Without the leak, the tank fills in 4 hours

With the leak, time = 4 hours + 30 minutes = 9/2 hours

(A + B − Leak)’s 1 hour work = 2/9

Leak’s 1 hour work = 1/4 − 2/9

= (9 − 8)/36 = 1/36

Hence, the leakage alone will empty the full tank in 36 hours.

Shortcut Method

Leak time = (t1 × t2)/(t2 − t1), where t1 = 4 and t2 = 4.5

= (4 × 4.5)/(4.5 − 4)

= 18/0.5

= 36 hours

Answer: (D) 36 hours

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Correct Answer: (A) 2 : 3

Explanation

HCF = 6, so let x = 6a and y = 6b (a and b co-prime)

LCM = 6ab = 36

ab = 6

Co-prime pairs (a, b) with a ≤ b: (1, 6) and (2, 3)

(1, 6) gives 6 and 36, but 6 is not a 2-digit number

(2, 3) gives x = 12 and y = 18 (both 2-digit)

x : y = 12 : 18 = 2 : 3

Hence, x : y is 2 : 3.

Shortcut Method

Product of numbers = LCM × HCF = 36 × 6 = 216

Check option (A): 2 : 3 gives 12 and 18, and 12 × 18 = 216

LCM(12, 18) = 36 and HCF(12, 18) = 6, so (A) is correct

Answer: (A) 2 : 3

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Correct Answer: (C) 8 km/hr

Explanation

Speed = 2 2/9 m/s = 20/9 m/s

1 m/s = 18/5 km/hr

Speed in km/hr = 20/9 × 18/5

= 360/45

= 8 km/hr

Hence, 2 2/9 m/s = 8 km/hr.

Shortcut Method

m/s to km/hr: multiply by 3.6

= (20/9) × 3.6 = 72/9

= 8 km/hr

Answer: (C) 8 km/hr

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Correct Answer: (A) 2

Explanation

Given number = 8270

Divisor = 16

8270 ÷ 16 = 516, remainder 14

(16 × 516 = 8256 and 8270 − 8256 = 14)

Least number to be added = Divisor − Remainder

= 16 − 14

= 2

Check: 8270 + 2 = 8272 = 16 × 517

Hence, the least positive integer to be added is 2.

Shortcut Method

8270 = 8000 + 270, and 8000 = 16 × 500 is already divisible

270 ÷ 16 leaves remainder 14 (16 × 16 = 256)

Number to add = 16 − 14 = 2

Answer: (A) 2

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Correct Answer: (A) ₹ 10,500

Explanation

Quantity of 1st coffee = 10 quintals at Rs. 8,000 per quintal

Quantity of 2nd coffee = 6 quintals at Rs. 10,000 per quintal

Cost of 1st coffee = 10 × 8,000 = Rs. 80,000

Cost of 2nd coffee = 6 × 10,000 = Rs. 60,000

Total cost of 16 quintals = 80,000 + 60,000 = Rs. 1,40,000

CP of mixture per quintal = 1,40,000 ÷ 16 = Rs. 8,750

Profit = 20%

SP = CP × (100 + Profit%)/100

= 8,750 × 120/100

= Rs. 10,500

Hence, the mixture must be sold at Rs. 10,500 per quintal.

Shortcut Method

Ratio 10 : 6 = 5 : 3

Average CP = (5 × 8,000 + 3 × 10,000)/8 = 70,000/8 = Rs. 8,750

SP = 8,750 × 1.2

= Rs. 10,500

Answer: (A) ₹ 10,500

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Correct Answer: (C) ₹ 1,120

Explanation

Marked Price (MP) = Rs. 4,000

First discount = 20%

Price after 1st discount = 4,000 × 80/100 = Rs. 3,200

Second discount = 10% on Rs. 3,200

Price after 2nd discount = 3,200 × 90/100 = Rs. 2,880

Amount saved = MP − Final price

= 4,000 − 2,880

= Rs. 1,120

Hence, the customer saves Rs. 1,120.

Shortcut Method

Equivalent discount = a + b − (a × b)/100

= 20 + 10 − (20 × 10)/100

= 28%

Saving = 28% of 4,000 = Rs. 1,120

Answer: (C) ₹ 1,120

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Correct Answer: (A) 10%

Explanation

Total population = 6000

Males = 3/12 × 6000 = 1500

Females = 6000 − 1500 = 4500

Married males = 30% of 1500 = (30/100) × 1500 = 450

Each married man has one wife, so married females = 450

Percentage of married females = (450/4500) × 100

= 10%

Hence, 10% of the females in the city are married.

Shortcut Method

Male : Female = 3/12 : 9/12 = 1 : 3

Married females % = 30% × (1/3)

= 10%

Answer: (A) 10%

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Correct Answer: (B) 30 days

Explanation

X is twice as good as Y

Efficiency of X = 2 units/day

Efficiency of Y = 1 unit/day

Together = 2 + 1 = 3 units/day

Total work = 3 × 20 = 60 units

Time taken by X alone = Total work ÷ Efficiency of X

= 60 ÷ 2

= 30 days

Hence, X alone will finish the work in 30 days.

Shortcut Method

X alone = Together time × (Sum of efficiencies)/(Efficiency of X)

= 20 × 3/2

= 30 days

Answer: (B) 30 days

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Correct Answer: (B) 5 km/hr

Explanation

Total distance = 6 km

Total time = 84 minutes

First part = 2/3 × 6 = 4 km at 4 km/hr

Time for first part = Distance ÷ Speed = 4 ÷ 4 = 1 hr = 60 minutes

Remaining distance = 6 − 4 = 2 km

Remaining time = 84 − 60 = 24 minutes = 24/60 hr = 2/5 hr

Required speed = Distance ÷ Time

= 2 ÷ 2/5

= 2 × 5/2

= 5 km/hr

Hence, the speed for the remaining distance is 5 km/hr.

Shortcut Method

Speed (km/hr) = Distance (km) × 60 ÷ Time (minutes)

= 2 × 60 ÷ 24

= 5 km/hr

Answer: (B) 5 km/hr

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Correct Answer: (C) 8 km/hr

Explanation

Downstream speed (D) = 11 km/hr

Upstream speed (U) = 5 km/hr

Speed of boat in still water = (D + U)/2

= (11 + 5)/2

= 16/2

= 8 km/hr

Speed of stream = (D − U)/2 = (11 − 5)/2 = 3 km/hr

Hence, the speed of the boat in still water is 8 km/hr.

Shortcut Method

Boat speed = average of downstream and upstream speeds

= (11 + 5)/2

= 8 km/hr

(3 km/hr, option A, is the speed of the stream)

Answer: (C) 8 km/hr

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Correct Answer: (C) 25 years

Explanation

Let present ages of Father, Mother and Son = 6x, 5x and x years

Son reaches father’s present age (6x) after = 6x − x = 5x years

After 5x years:

Father = 6x + 5x = 11x

Mother = 5x + 5x = 10x

Son = x + 5x = 6x

Sum = 11x + 10x + 6x = 27x

27x = 135

x = 5

Mother’s present age = 5x = 5 × 5 = 25 years

Hence, the present age of the mother is 25 years.

Shortcut Method

Present sum = 6x + 5x + x = 12x; each of 3 persons gains 5x years

12x + 3 × 5x = 27x = 135, so x = 5

Mother = 5 × 5 = 25 years

Answer: (C) 25 years

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Correct Answer: (D) 25

Explanation

Number of values = 10

Average = 20

Sum = 10 × 20 = 200

Increase in sum = 10 × 5 = 50

New sum = 200 + 50 = 250

New average = 250 ÷ 10

= 25

Hence, the new average is 25.

Shortcut Method

If every number increases by 5, the average also increases by 5

New average = 20 + 5

= 25

Answer: (D) 25

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Correct Answer: (D) 32

Explanation

Total questions = 62 (all attempted)

Let correct answers = c

Wrong answers = 62 − c

Marks = 2 × correct − 1 × wrong

2c − (62 − c) = 34

3c − 62 = 34

3c = 96

c = 32

Check: 32 × 2 − 30 × 1 = 64 − 30 = 34

Hence, Ramen answered 32 questions correctly.

Shortcut Method

If all 62 were correct, marks = 62 × 2 = 124

Each wrong answer loses 2 + 1 = 3 marks

Wrong = (124 − 34) ÷ 3 = 30

Correct = 62 − 30 = 32

Answer: (D) 32

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Correct Answer: (A) 7·5 days

Explanation

Total work = 20 men × 10 days = 200 man-days

Work done in first 5 days = 20 × 5 = 100 man-days

Remaining work = 200 − 100 = 100 man-days

Men after 5 days = 20 + 20 = 40

Days for remaining work = 100 ÷ 40 = 2.5 days

Total days = 5 + 2.5

= 7.5 days

Hence, the entire job is completed in 7.5 days.

Shortcut Method

In 5 days, half the job is done (5/10)

Men are doubled, so the other half takes half the time = 5 ÷ 2 = 2.5 days

Total = 5 + 2.5 = 7.5 days

Answer: (A) 7·5 days

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Correct Answer: (D) 131

Explanation

The differences between terms are 11 − 7 = 4, 19 − 11 = 8, 35 − 19 = 16, 67 − 35 = 32, i.e. they double each time. The next difference is 64, so the next term is 67 + 64 = 131, option (D).

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Correct Answer: (B) Sunday

Explanation

If the day after tomorrow is Saturday, then today is Thursday. So yesterday was Wednesday, and 3 days before Wednesday is Sunday (Wednesday → Tuesday → Monday → Sunday). The answer is (B) Sunday.

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Correct Answer: (A) 8 : 12 : 15 : 35

Explanation

A : B = 2 : 3

B : C = 4 : 5

C : D = 3 : 7

Make B equal in the first two ratios (LCM of 3 and 4 = 12)

A : B = 2 × 4 : 3 × 4 = 8 : 12

B : C = 4 × 3 : 5 × 3 = 12 : 15

So A : B : C = 8 : 12 : 15

Make C equal (C = 15, so multiply C : D by 5)

C : D = 3 × 5 : 7 × 5 = 15 : 35

A : B : C : D = 8 : 12 : 15 : 35

Hence, A : B : C : D = 8 : 12 : 15 : 35.

Shortcut Method

A = 2 × 4 × 3 = 24

B = 3 × 4 × 3 = 36

C = 3 × 5 × 3 = 45

D = 3 × 5 × 7 = 105

A : B : C : D = 24 : 36 : 45 : 105 = 8 : 12 : 15 : 35

Answer: (A) 8 : 12 : 15 : 35

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Correct Answer: (B) 4.5 km/hr

Explanation

Upstream distance = 9 km in 3 hrs

Upstream speed (U) = 9/3 = 3 km/hr

Downstream distance = 18 km in 3 hrs

Downstream speed (D) = 18/3 = 6 km/hr

Speed of boat in still water = (D + U)/2

= (6 + 3)/2

= 4.5 km/hr

Hence, the speed of the boat in still water is 4.5 km/hr.

Shortcut Method

Boat speed = (18 + 9)/(2 × 3)

= 27/6

= 4.5 km/hr

Answer: (B) 4.5 km/hr

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Correct Answer: (A) 5 1/7 hours

Explanation

Pipe A fills the tank in 9 hours, so in 1 hour it fills 1/9

Pipe B fills the tank in 12 hours, so in 1 hour it fills 1/12

Work of both in 1 hour = 1/9 + 1/12

= (4 + 3)/36

= 7/36

Time taken by both = 36/7 hours

= 5 1/7 hours

Hence, the tank will be filled in 5 1/7 hours.

Shortcut Method

Time = (a × b)/(a + b)

= (9 × 12)/(9 + 12)

= 108/21

= 5 1/7 hours

Answer: (A) 5 1/7 hours

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Correct Answer: (D) 16

Explanation

Let the three consecutive even integers be x, x + 2 and x + 4

Sum = x + (x + 2) + (x + 4) = 54

3x + 6 = 54

3x = 48

x = 16

Numbers are 16, 18 and 20

Hence, the least number is 16.

Shortcut Method

Middle number = Sum/3 = 54/3 = 18

Least number = 18 − 2

= 16

Answer: (D) 16

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Correct Answer: (C) 2835

Explanation

Let the numbers be 5x and 7x

LCM of 5x and 7x = 35x

35x = 315

x = 9

Numbers = 5 × 9 = 45 and 7 × 9 = 63

Product = 45 × 63

= 2835

Hence, the product of the numbers is 2835.

Shortcut Method

HCF = x = 9

Product = HCF × LCM

= 9 × 315

= 2835

Answer: (C) 2835

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Correct Answer: (A) 10 gms

Explanation

Total solution = 150 gm

Sugar = 20% of 150 = (20/100) × 150 = 30 gm

Water = 150 − 30 = 120 gm

After adding sugar, water stays 120 gm and becomes 75% of the new solution

New solution = 120 × (100/75)

= 160 gm

Sugar to be added = 160 − 150

= 10 gm

Hence, 10 gm of sugar should be added.

Shortcut Method

Sugar added = Solution × (New% − Old%)/(100 − New%)

= 150 × (25 − 20)/(100 − 25)

= 150 × 5/75

= 10 gm

Answer: (A) 10 gms

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Correct Answer: (C) 48 kmph

Explanation

Speed from P to Q = 40 kmph

Return speed = 40 + 50% of 40 = 40 + 20 = 60 kmph

Distance is the same both ways

Average speed = 2xy/(x + y)

= (2 × 40 × 60)/(40 + 60)

= 4800/100

= 48 kmph

Hence, his average speed for both the trips is 48 kmph.

Shortcut Method

Take distance = LCM of 40 and 60 = 120 km

Total time = 120/40 + 120/60 = 3 + 2 = 5 hrs

Average speed = 240/5

= 48 kmph

Answer: (C) 48 kmph

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Correct Answer: (B) 9 3/8 days

Explanation

A does 1/3 of the work in 5 days

A does the whole work in 5 × 3 = 15 days

B does 2/5 of the work in 10 days

B does the whole work in 10 × (5/2) = 25 days

Work of A and B in 1 day = 1/15 + 1/25

= (5 + 3)/75

= 8/75

Time taken together = 75/8 days

= 9 3/8 days

Hence, A and B together can do the work in 9 3/8 days.

Shortcut Method

Time = (a × b)/(a + b)

= (15 × 25)/(15 + 25)

= 375/40

= 9 3/8 days

Answer: (B) 9 3/8 days

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Correct Answer: (B) 1141

Explanation

Required number = LCM of 57, 76 and 190 + 1

57 = 3 × 19

76 = 2 × 2 × 19

190 = 2 × 5 × 19

LCM = 2 × 2 × 3 × 5 × 19

= 1140

Required number = 1140 + 1

= 1141

Hence, the smallest number is 1141.

Shortcut Method

All three numbers are multiples of 19: 57 = 19 × 3, 76 = 19 × 4, 190 = 19 × 10

LCM = 19 × LCM(3, 4, 10) = 19 × 60 = 1140

Number = 1140 + 1 = 1141

Answer: (B) 1141

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Correct Answer: (D) 9.75

Explanation

Let the number be x

(2/3) × x = 26

x = 26 × (3/2)

x = 39

25% of 39 = (25/100) × 39

= 39/4

= 9.75

Hence, 25% of the number is 9.75.

Shortcut Method

1/3 of the number = 26/2 = 13

Number = 39

25% = 1/4 of 39 = 9.75

Answer: (D) 9.75

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Correct Answer: (B) Rs. 150

Explanation

Principal (P) = Rs. 500

Rate (R) = 5% per annum

Time (T) = 6 years

Simple Interest (SI) = (P × R × T)/100

= (500 × 5 × 6)/100

= 15000/100

= Rs. 150

Hence, the simple interest is Rs. 150.

Shortcut Method

Total rate = R × T = 5 × 6 = 30%

SI = 30% of 500

= Rs. 150

Answer: (B) Rs. 150

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Correct Answer: (C) 16/9

Explanation

5 5/3 = (5 × 3 + 5)/3 = 20/3 = 60/9

3 8/9 = (3 × 9 + 8)/9 = 35/9

60/9 − 35/9 − * = 1

25/9 − * = 1

* = 25/9 − 1

= 25/9 − 9/9

= 16/9

Hence, the value in place of * is 16/9.

Shortcut Method

5 5/3 = 6 2/3 = 6 6/9

6 6/9 − 3 8/9 = 2 7/9

* = 2 7/9 − 1 = 1 7/9 = 16/9

Answer: (C) 16/9

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Correct Answer: (A) 7 1/2 days

Explanation

A does the work in 12 days

B is 60% more efficient than A

Efficiency of A : Efficiency of B = 100 : 160 = 5 : 8

Time is inversely proportional to efficiency

Time of A : Time of B = 8 : 5

Time of B = 12 × (5/8)

= 60/8

= 7 1/2 days

Hence, B will finish the work in 7 1/2 days.

Shortcut Method

Time of B = 12 × 100/160

= 12/1.6

= 7.5 days

Answer: (A) 7 1/2 days

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Correct Answer: (B) 37%

Explanation

Let the marked price be Rs. 100

After first discount of 10% = 100 − 10 = Rs. 90

Second discount of 30% on 90 = (30/100) × 90 = Rs. 27

Final price = 90 − 27 = Rs. 63

Total discount = 100 − 63 = Rs. 37

Single equivalent discount = 37%

Hence, the single equivalent discount is 37%.

Shortcut Method

Single discount = a + b − (a × b)/100

= 10 + 30 − (10 × 30)/100

= 40 − 3

= 37%

Answer: (B) 37%

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Correct Answer: (D) Rs. 13,310

Explanation

Principal (P) = Rs. 10,000

Rate (R) = 10% per annum, compounded annually

Time (n) = 3 years

Amount (A) = P × (1 + R/100)^n

= 10000 × (1 + 10/100)^3

= 10000 × (11/10)^3

= 10000 × 1331/1000

= Rs. 13,310

Hence, the amount is Rs. 13,310.

Shortcut Method

Year 1: 10000 + 1000 = 11000

Year 2: 11000 + 1100 = 12100

Year 3: 12100 + 1210 = Rs. 13,310

Answer: (D) Rs. 13,310

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Correct Answer: (B) 2

Explanation

Let a = 2.3 and b = 0.3

Then 0.027 = 0.3 × 0.3 × 0.3 = b^3

0.69 = 2.3 × 0.3 = a × b

0.09 = 0.3 × 0.3 = b^2

Expression = (a^3 − b^3)/(a^2 + ab + b^2)

Formula: a^3 − b^3 = (a − b)(a^2 + ab + b^2)

Expression = a − b

= 2.3 − 0.3

= 2

Hence, the simplified value is 2.

Shortcut Method

(a^3 − b^3)/(a^2 + ab + b^2) = a − b

= 2.3 − 0.3

= 2

Answer: (B) 2

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Correct Answer: (C) 50

Explanation

50% of P = 25% of Q

(50/100) × P = (25/100) × Q

P = (25/50) × Q

P = (1/2) × Q

P = 50% of Q

So x = 50

Hence, the value of x is 50.

Shortcut Method

x = (25/50) × 100

= 50

Answer: (C) 50

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Correct Answer: (A) 595

Explanation

Let the numbers be 10x and 7x

Difference = 10x − 7x = 105

3x = 105

x = 35

Numbers = 10 × 35 = 350 and 7 × 35 = 245

Sum = 350 + 245

= 595

Hence, the sum of the numbers is 595.

Shortcut Method

Difference of ratio terms = 10 − 7 = 3 parts = 105, so 1 part = 35

Sum = 17 parts = 17 × 35

= 595

Answer: (A) 595

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Correct Answer: (D) 21% profit

Explanation

Cost Price (CP) of 1 apple = Rs. 10/11

Selling Price (SP) of 1 apple = Rs. 11/10

SP/CP = (11/10) ÷ (10/11)

= (11/10) × (11/10)

= 121/100

Profit% = (121 − 100)/100 × 100

= 21%

Hence, he made a profit of 21%.

Shortcut Method

Take LCM of apples = 110

CP of 110 apples = 10 × 10 = Rs. 100

SP of 110 apples = 11 × 11 = Rs. 121

Profit = 21 on 100 = 21% profit

Answer: (D) 21% profit

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Correct Answer: (B) 32 years

Explanation

Ratio of ages A : B : C = 5 : 8 : 9

Let the ages be 5x, 8x and 9x

A + C = 5x + 9x = 56

14x = 56

x = 4

Age of B = 8x = 8 × 4

= 32 years

Hence, the age of B is 32 years.

Shortcut Method

A + C = 5 + 9 = 14 parts = 56, so 1 part = 4

B = 8 parts = 8 × 4

= 32 years

Answer: (B) 32 years

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Correct Answer: (B) 7

Explanation

Let the number = 175k + 132

175 is divisible by 25 (175 = 25 × 7)

So 175k leaves remainder 0 when divided by 25

Remainder = remainder of 132 ÷ 25

132 = 25 × 5 + 7

Remainder = 7

Hence, the remainder is 7.

Shortcut Method

Since 25 divides 175, remainder = 132 ÷ 25

= 5 remainder 7

Answer = 7

Answer: (B) 7

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Correct Answer: (D) 0.36

Explanation

Expression = 0.2 + 0.2 − 0.2 ÷ 0.2 × (0.2 × 0.2)

Apply BODMAS: Bracket first

0.2 × 0.2 = 0.04

= 0.2 + 0.2 − 0.2 ÷ 0.2 × 0.04

Division next: 0.2 ÷ 0.2 = 1

= 0.2 + 0.2 − 1 × 0.04

Multiplication next: 1 × 0.04 = 0.04

= 0.4 − 0.04

= 0.36

Hence, the simplified value is 0.36.

Shortcut Method

0.2 ÷ 0.2 = 1, so the expression = 0.4 − 0.04

= 0.36

Answer: (D) 0.36

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Correct Answer: (D) 200%

Explanation

Let the Principal (P) = 1

Amount (A) = 27 × P = 27

Time (n) = 3 years

A = P × (1 + R/100)^n

27 = 1 × (1 + R/100)^3

3^3 = (1 + R/100)^3

1 + R/100 = 3

R/100 = 2

R = 200%

Hence, the rate of interest is 200% per annum.

Shortcut Method

Cube root of 27 = 3, so money triples every year

Rate = (3 − 1) × 100

= 200%

Answer: (D) 200%

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Correct Answer: (D) 0.3

Explanation

√0.0049 = 0.07 (since 0.07 × 0.07 = 0.0049)

√(0.02 + √0.0049) = √(0.02 + 0.07)

= √0.09

= 0.3 (since 0.3 × 0.3 = 0.09)

Hence, the value is 0.3.

Shortcut Method

√49 = 7, so √0.0049 = 0.07

0.02 + 0.07 = 0.09

√0.09 = 0.3

Answer: (D) 0.3

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Correct Answer: (C) 9

Explanation

Number = 5 7 9 * 2

Divisibility rule of 11: (sum of digits at odd places) − (sum of digits at even places) = 0 or a multiple of 11

Odd places from right (1st, 3rd, 5th): 2 + 9 + 5 = 16

Even places from right (2nd, 4th): * + 7

16 − (* + 7) = 0

9 − * = 0

* = 9

Check: 57992 ÷ 11 = 5272

Hence, the digit in place of * is 9.

Shortcut Method

Option D (11) is not a single digit, so it is out

Try 9: 2 + 9 + 5 = 16 and 9 + 7 = 16

Difference = 0, so * = 9

Answer: (C) 9

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Correct Answer: (B) 24/19 m/sec

Explanation

Speed of A = 5 km/hr

= 5 × 5/18 m/sec

= 25/18 m/sec

Time taken by A for 200 m = 200 ÷ (25/18)

= 200 × 18/25

= 144 sec

B gets a start of 8 m, so distance run by B = 200 − 8 = 192 m

A beats B by 8 sec, so time taken by B = 144 + 8 = 152 sec

Speed of B = Distance/Time

= 192/152

= 24/19 m/sec

Hence, the speed of B is 24/19 m/sec.

Shortcut Method

Speed of B = (200 − start) ÷ (time of A + 8)

= 192 ÷ (200 × 18/25 + 8)

= 192 ÷ 152

= 24/19 m/sec

Answer: (B) 24/19 m/sec

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Correct Answer: (D) 3 3/7 days

Explanation

A’s 1 day work = 1/6

B’s 1 day work = 1/12

C’s 1 day work = 1/24

(A + B + C)’s 1 day work = 1/6 + 1/12 + 1/24

= (4 + 2 + 1)/24

= 7/24

Time taken together = 24/7 days

= 3 3/7 days

Hence, A, B and C together will complete the work in 3 3/7 days.

Shortcut Method

Total work = LCM of 6, 12, 24 = 24 units

Efficiency of A, B, C = 4, 2, 1 units/day

Together = 4 + 2 + 1 = 7 units/day

Time = 24/7 = 3 3/7 days

Quick check: together they must finish faster than A alone (6 days), and only 3 3/7 days is less than 6.

Answer: (D) 3 3/7 days

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Correct Answer: (B) 4%

Explanation

Amount after 5 years = Rs. 600

Amount after 3 years = Rs. 560

SI for 2 years = 600 − 560 = Rs. 40

SI for 1 year = 40/2 = Rs. 20

SI for 3 years = 20 × 3 = Rs. 60

Principal (P) = 560 − 60 = Rs. 500

Rate (R) = (SI × 100)/(P × T)

= (20 × 100)/(500 × 1)

= 4%

Hence, the rate of interest is 4% per annum.

Shortcut Method

P = (A1 × T2 − A2 × T1)/(T2 − T1)

= (560 × 5 − 600 × 3)/(5 − 3)

= (2800 − 1800)/2 = Rs. 500

R = (20/500) × 100 = 4%

Answer: (B) 4%

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Correct Answer: (D) 2.13

Explanation

√0.01 = 0.1

√0.81 = 0.9

√1.21 = 1.1

√0.0009 = 0.03

Sum = 0.1 + 0.9 + 1.1 + 0.03

= 2.1 + 0.03

= 2.13

Hence, the value is 2.13.

Shortcut Method

Square root of a decimal has half the number of decimal places

√0.0009 = √9 with 4/2 = 2 decimal places = 0.03

0.1 + 0.9 + 1.1 = 2.1

2.1 + 0.03 = 2.13

Answer: (D) 2.13

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Correct Answer: (B) 10%

Explanation

Let Cost Price (CP) = 10x and Selling Price (SP) = 11x

Profit = SP − CP

= 11x − 10x

= x

Profit % = (Profit/CP) × 100

= (x/10x) × 100

= 10%

Hence, the profit is 10%.

Shortcut Method

Profit % = (SP term − CP term)/CP term × 100

= (11 − 10)/10 × 100

= 10%

Answer: (B) 10%

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Correct Answer: (B) 100%

Explanation

Let Principal = P, Amount after 2 years = 4P, Rate = R% p.a.

Formula: A = P × (1 + R/100)^n

4P = P × (1 + R/100)^2

(1 + R/100)^2 = 4

1 + R/100 = 2

R/100 = 1

R = 100%

Hence, the rate of interest is 100% per annum.

Shortcut Method

Sum becomes x times in n years: R = (x^(1/n) − 1) × 100

= (√4 − 1) × 100

= (2 − 1) × 100 = 100%

Answer: (B) 100%

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Correct Answer: (D) 5 5/11 days

Explanation

A does 1/2 work in 5 days

A alone does full work in 5 × 2 = 10 days

B does 1/3 work in 4 days

B alone does full work in 4 × 3 = 12 days

(A + B)’s 1 day work = 1/10 + 1/12

= (6 + 5)/60

= 11/60

Time taken together = 60/11 days

= 5 5/11 days

Hence, working together they finish the work in 5 5/11 days.

Shortcut Method

Together time = (a × b)/(a + b)

= (10 × 12)/(10 + 12)

= 120/22 = 60/11 = 5 5/11 days

Answer: (D) 5 5/11 days

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Correct Answer: (C) 3%

Explanation

1 minute 48 seconds = 60 + 48 = 108 seconds

1 hour = 60 × 60 = 3600 seconds

Required per cent = (108/3600) × 100

= 10800/3600

= 3%

Hence, 1 minute 48 seconds is 3% of an hour.

Shortcut Method

1 minute 48 seconds = 1.8 minutes

Per cent = (1.8/60) × 100

= 180/60 = 3%

Answer: (C) 3%

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Correct Answer: (B) 13.5 seconds

Explanation

Length of train = 60 m

Length of platform = 90 m

Total distance to cover = 60 + 90 = 150 m

Speed = 40 km/hr = 40 × 5/18 m/s = 100/9 m/s

Time = Distance / Speed

= 150 ÷ (100/9)

= 150 × 9/100

= 13.5 seconds

Hence, the train crosses the platform in 13.5 seconds.

Shortcut Method

Time = (Total length × 18)/(Speed in km/hr × 5)

= (150 × 18)/(40 × 5)

= 2700/200 = 13.5 seconds

Answer: (B) 13.5 seconds

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Correct Answer: (A) 56.25% profit

Explanation

CP of 15 apples = Rs. 12

CP of 1 apple = 12/15 = Rs. 0.80

SP of 12 apples = Rs. 15

SP of 1 apple = 15/12 = Rs. 1.25

Profit per apple = 1.25 − 0.80 = Rs. 0.45

Profit % = (Profit/CP) × 100

= (0.45/0.80) × 100

= 56.25%

Hence, the fruit seller made a profit of 56.25%.

Shortcut Method

Profit % = [(SP per item/CP per item) − 1] × 100

= [(15/12) ÷ (12/15) − 1] × 100

= [(15 × 15)/(12 × 12) − 1] × 100

= (225/144 − 1) × 100 = (81/144) × 100 = 56.25% profit

Answer: (A) 56.25% profit

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Correct Answer: (B) 2984

Explanation

Expression = 3034 − (1002 ÷ 20.04)

First solve the bracket (BODMAS)

1002 ÷ 20.04 = 100200 ÷ 2004

= 50

Expression = 3034 − 50

= 2984

Hence, the value of the expression is 2984.

Shortcut Method

20.04 × 50 = 1002, so 1002 ÷ 20.04 = 50

= 3034 − 50 = 2984

Answer: (B) 2984

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Correct Answer: (B) 40%

Explanation

First discount = 20%, Second discount = 25%

Let marked price = Rs. 100

Price after 20% discount = 100 − 20 = Rs. 80

Price after 25% discount on 80 = 80 − (25/100) × 80

= 80 − 20

= Rs. 60

Total discount = 100 − 60 = Rs. 40 on Rs. 100

Single equivalent discount = 40%

Hence, the single equivalent discount is 40%.

Shortcut Method

Single discount = a + b − (a × b)/100

= 20 + 25 − (20 × 25)/100

= 45 − 5 = 40%

Answer: (B) 40%

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Correct Answer: (A) 13 1/23 %

Explanation

Let Selling Price (SP) = Rs. 100

Loss = 15% of SP = Rs. 15

Cost Price (CP) = SP + Loss

= 100 + 15

= Rs. 115

Loss % on CP = (Loss/CP) × 100

= (15/115) × 100

= 300/23

= 13 1/23 %

Hence, the loss on cost price is 13 1/23 %.

Shortcut Method

Loss % on CP = x/(100 + x) × 100, where x = loss % on SP

= 15/115 × 100

= 300/23 = 13 1/23 %

Answer: (A) 13 1/23 %

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Correct Answer: (B) 25 years

Explanation

Let the ages be 7x, 5x and 4x years

Sum of first and third = 7x + 4x = 11x

Double of second = 2 × 5x = 10x

Given: 11x = 10x + 5

x = 5

Age of second person = 5x = 5 × 5

= 25 years

Hence, the age of the second person is 25 years.

Shortcut Method

Difference in ratio units = (7 + 4) − 2 × 5 = 1 unit

1 unit = 5 years

Second person = 5 units = 25 years

Answer: (B) 25 years

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Correct Answer: (B) 1261

Explanation

Required number = LCM of (20, 42, 63) + 1

20 = 2^2 × 5

42 = 2 × 3 × 7

63 = 3^2 × 7

LCM = 2^2 × 3^2 × 5 × 7

= 4 × 9 × 35

= 1260

Required number = 1260 + 1 = 1261

Hence, the smallest such number is 1261.

Shortcut Method

Option check: number − 1 must be divisible by 20, 42 and 63

1261 − 1 = 1260 = 20 × 63 = 42 × 30

Other options − 1 = 1240, 1258, 1238, none divisible by 63, so 1261

Answer: (B) 1261

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Correct Answer: (C) 15 1/6

Explanation

20 1/2 + 30 1/3 − * = 35 2/3

* = 20 1/2 + 30 1/3 − 35 2/3

Whole numbers: 20 + 30 − 35 = 15

Fractions: 1/2 + 1/3 − 2/3

= 3/6 + 2/6 − 4/6

= 1/6

* = 15 + 1/6

= 15 1/6

Hence, the value in place of * is 15 1/6.

Shortcut Method

Whole part = 20 + 30 − 35 = 15

Fraction part = 1/2 + 1/3 − 2/3 = 1/2 − 1/3 = 1/6

= 15 1/6

Answer: (C) 15 1/6

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Correct Answer: (D) 16 2/3 %

Explanation

Let original price = Rs. 100 per unit and consumption = 100 units

Original expenditure = 100 × 100 = Rs. 10000

New price = 100 + 20% of 100 = Rs. 120

New consumption = 10000 ÷ 120

= 83 1/3 units

Decrease in consumption = 100 − 83 1/3

= 16 2/3 units out of 100

Hence, the family should reduce consumption by 16 2/3 %.

Shortcut Method

Reduction % = R/(100 + R) × 100

= 20/120 × 100

= 50/3 = 16 2/3 %

Answer: (D) 16 2/3 %

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Correct Answer: (A) 12 minutes

Explanation

First tap empties the tank in 30 minutes

Work of first tap in 1 minute = 1/30

Second tap empties the tank in 20 minutes

Work of second tap in 1 minute = 1/20

Both taps in 1 minute = 1/30 + 1/20

= (2 + 3)/60

= 5/60 = 1/12

Time to empty = 12 minutes

Hence, both taps together empty the cistern in 12 minutes.

Shortcut Method

Time = (a × b)/(a + b)

= (30 × 20)/(30 + 20)

= 600/50 = 12 minutes

Answer: (A) 12 minutes

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Correct Answer: (B) 50/11 %

Explanation

Amount in 5 years = Rs. 540

Amount in 3 years = Rs. 500

SI for 2 years = 540 − 500 = Rs. 40

SI for 1 year = 40/2 = Rs. 20

SI for 3 years = 20 × 3 = Rs. 60

Principal (P) = 500 − 60 = Rs. 440

Rate (R) = (SI × 100)/(P × T)

= (20 × 100)/(440 × 1)

= 2000/440

= 50/11 %

Hence, the rate of interest is 50/11 % per annum.

Shortcut Method

R = (A2 − A1) × 100/(A1 × T2 − A2 × T1)

= (540 − 500) × 100/(500 × 5 − 540 × 3)

= 4000/(2500 − 1620) = 4000/880 = 50/11 %

Answer: (B) 50/11 %

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Correct Answer: (C) 60 gms

Explanation

Total solution = 300 gm

Sugar = 40% of 300 = 120 gm

Water = 300 − 120 = 180 gm

Let x gm sugar be added

New sugar = 120 + x, New solution = 300 + x

(120 + x)/(300 + x) = 50/100 = 1/2

2(120 + x) = 300 + x

240 + 2x = 300 + x

x = 60 gm

Hence, 60 gm of sugar should be added.

Shortcut Method

Water stays 180 gm and must become 50% of the new solution

New solution = 180 × 2 = 360 gm

Sugar added = 360 − 300 = 60 gm

Answer: (C) 60 gms

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Correct Answer: (A) 8

Explanation

Number = 4 5 3 3 7 * 2

Rule: a number is divisible by 11 if (sum of digits at odd places) − (sum of digits at even places) is 0 or a multiple of 11

Digits at odd places from right: 2, 7, 3, 4

Sum = 2 + 7 + 3 + 4 = 16

Digits at even places from right: *, 3, 5

Sum = * + 3 + 5 = * + 8

Difference = 16 − (* + 8) = 8 − *

For divisibility, 8 − * = 0

* = 8

Hence, the digit in place of * is 8.

Shortcut Method

Odd-place sum = 16, even-place sum without * = 8

* = 16 − 8 = 8

Check: 4533782 ÷ 11 = 412162

Answer: (A) 8

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Correct Answer: (B) Rs. 676

Explanation

Principal (P) = Rs. 625, Rate (R) = 4% p.a., Time (n) = 2 years

Formula: A = P × (1 + R/100)^n

A = 625 × (1 + 4/100)^2

= 625 × (26/25)^2

= 625 × 676/625

= Rs. 676

Hence, the amount is Rs. 676.

Shortcut Method

Effective rate for 2 years = 4 + 4 + (4 × 4)/100 = 8.16%

A = 625 + 8.16% of 625

= 625 + 51 = Rs. 676

Answer: (B) Rs. 676

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Correct Answer: (C) 8 : 6 : 10 : 9

Explanation

A : B = 4 : 3

B : C = 3 : 5

B is 3 in both, so A : B : C = 4 : 3 : 5

C : D = 10 : 9

Make C equal: multiply A : B : C by 2

A : B : C = 8 : 6 : 10

A : B : C : D = 8 : 6 : 10 : 9

Hence, A : B : C : D = 8 : 6 : 10 : 9.

Shortcut Method

A : B : C : D = (4 × 3 × 10) : (3 × 3 × 10) : (3 × 5 × 10) : (3 × 5 × 9)

= 120 : 90 : 150 : 135

= 8 : 6 : 10 : 9

Answer: (C) 8 : 6 : 10 : 9

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Correct Answer: (C) 15 days

Explanation

A does the work in 21 days

Let A’s efficiency = 100

B’s efficiency = 100 + 40 = 140

Efficiency ratio A : B = 100 : 140 = 5 : 7

Time ratio A : B = 7 : 5 (time is inverse of efficiency)

B’s time = 21 × 5/7

= 15 days

Hence, B will finish the work in 15 days.

Shortcut Method

Time of B = Time of A × 100/(100 + 40)

= 21 × 100/140

= 15 days

Answer: (C) 15 days

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Correct Answer: (C) 0.7

Explanation

√0.0064 = 0.08

0.01 + 0.08 = 0.09

√0.09 = 0.3

√0.16 = 0.4

Value = 0.3 + 0.4

= 0.7

Hence, the value of the expression is 0.7.

Shortcut Method

√(0.01 + 0.08) + 0.4

= √0.09 + 0.4

= 0.3 + 0.4 = 0.7

Answer: (C) 0.7

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Correct Answer: (D) 2160

Explanation

Ratio of numbers = 3 : 5, HCF = 12

First number = 3 × 12 = 36

Second number = 5 × 12 = 60

Product = 36 × 60

= 2160

Hence, the product of the two numbers is 2160.

Shortcut Method

Product = HCF^2 × (product of ratio terms)

= 12^2 × 3 × 5

= 144 × 15 = 2160

Answer: (D) 2160

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Correct Answer: (C) 13

Explanation

Let a = 8.73 and b = 4.27

Numerator = a × a × a + b × b × b = a^3 + b^3

Denominator = a × a + b × b − a × b = a^2 + b^2 − ab

Formula: a^3 + b^3 = (a + b)(a^2 − ab + b^2)

Expression = (a + b)(a^2 − ab + b^2) / (a^2 − ab + b^2)

= a + b

= 8.73 + 4.27

= 13

Hence, the simplified value is 13.

Shortcut Method

(a^3 + b^3) / (a^2 − ab + b^2) = a + b

= 8.73 + 4.27

= 13

Answer: (C) 13

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Correct Answer: (C) 50

Explanation

Given: 60% of P = 30% of Q

(60/100) × P = (30/100) × Q

60P = 30Q

P = (30/60) × Q

= (1/2) × Q

= (50/100) × Q

= 50% of Q

So, x = 50

Hence, the value of x is 50.

Shortcut Method

x = (30 ÷ 60) × 100

= 0.5 × 100

= 50

Answer: (C) 50

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Correct Answer: (B) Rs. 120

Explanation

Principal (P) = Rs. 400

Rate (R) = 6% per annum

Time (T) = 5 years

Simple Interest (SI) = (P × R × T)/100

= (400 × 6 × 5)/100

= 12000/100

= Rs. 120

Hence, the simple interest is Rs. 120.

Shortcut Method

SI for 1 year = 6% of 400 = Rs. 24

SI for 5 years = 24 × 5

= Rs. 120

Answer: (B) Rs. 120

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Correct Answer: (B) 23

Explanation

Let the 7 consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6

Sum = 7x + 21

Average = Sum/7

20 = (7x + 21)/7

140 = 7x + 21

7x = 119

x = 17

Largest number = x + 6

= 17 + 6

= 23

Hence, the largest of these numbers is 23.

Shortcut Method

For consecutive numbers, average = middle (4th) number = 20

Largest = 4th number + 3

= 20 + 3

= 23

Answer: (B) 23

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Correct Answer: (D) 5 km/hr

Explanation

Distance = 24 km

Downstream Speed = 24/4 = 6 km/hr

Upstream Speed = 24/6 = 4 km/hr

Speed of boat in still water = (Downstream Speed + Upstream Speed)/2

= (6 + 4)/2

= 10/2

= 5 km/hr

Hence, the speed of the boat in still water is 5 km/hr.

Shortcut Method

Still water speed = (24/4 + 24/6)/2

= (6 + 4)/2

= 5 km/hr

Answer: (D) 5 km/hr

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Correct Answer: (B) 13.5

Explanation

Let the number be N

(2/3) × N = 36

N = 36 × (3/2)

= 54

25% of N = (25/100) × 54

= 54/4

= 13.5

Hence, 25% of the number is 13.5.

Shortcut Method

25% of N = (1/4) × N and N = 36 × 3/2

Required value = 36 × (3/2) × (1/4)

= 36 × 3/8

= 13.5

Answer: (B) 13.5

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Correct Answer: (A) 2

Explanation

Let the number be N

N = 119 × q + 19 (q = quotient)

119 = 17 × 7, so 119 × q is exactly divisible by 17

Remainder of N ÷ 17 = Remainder of 19 ÷ 17

19 = 17 × 1 + 2

= 2

Hence, the remainder when the number is divided by 17 is 2.

Shortcut Method

If the first divisor (119) is a multiple of the second divisor (17),

Required remainder = remainder of (first remainder ÷ second divisor)

= remainder of (19 ÷ 17)

= 2

Answer: (A) 2

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Correct Answer: (D) 26 2/3 kmph

Explanation

Speed from A to B (x) = 40 kmph

Return speed = 40 − 50% of 40 = 40 − 20 = 20 kmph (y)

Let the distance AB = 40 km (any value)

Time from A to B = 40/40 = 1 hour

Time from B to A = 40/20 = 2 hours

Average Speed = Total Distance/Total Time

= (40 + 40)/(1 + 2)

= 80/3

= 26 2/3 kmph

Hence, his average speed for both the trips is 26 2/3 kmph.

Shortcut Method

Average Speed (same distance) = 2xy/(x + y)

= (2 × 40 × 20)/(40 + 20)

= 1600/60

= 26 2/3 kmph

Answer: (D) 26 2/3 kmph

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Correct Answer: (D) 8/5 m/sec

Explanation

Speed of A = 8 km/hr = 8 × (5/18) m/sec = 20/9 m/sec

Time taken by A to run 100 m = 100 ÷ (20/9)

= 100 × 9/20

= 45 sec

B gets a start of 4 m, so B runs 100 − 4 = 96 m

A beats B by 15 sec, so time taken by B = 45 + 15 = 60 sec

Speed of B = Distance/Time

= 96/60

= 8/5 m/sec

Hence, the speed of B is 8/5 m/sec (1.6 m/sec).

Shortcut Method

Time of A = 100/(8 × 5/18) = 45 sec

Speed of B = (100 − 4)/(45 + 15)

= 96/60

= 8/5 m/sec

Answer: (D) 8/5 m/sec

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Correct Answer: (C) 52 years

Explanation

Let the present age of the father = F years and of the son = S years

F + S = 80

4 years ago, sum of their ages = 80 − 4 − 4 = 72 years

Ratio of their ages 4 years ago = 2 : 1

Father’s age 4 years ago = (2/3) × 72 = 48 years

Son’s age 4 years ago = (1/3) × 72 = 24 years

Father’s present age = 48 + 4

= 52 years

Check: Son’s present age = 24 + 4 = 28, and 52 + 28 = 80

Hence, the present age of the father is 52 years.

Shortcut Method

Sum 4 years ago = 80 − 2 × 4 = 72

Father then = 72 × 2/3 = 48

Father now = 48 + 4

= 52 years

Answer: (C) 52 years

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Correct Answer: (B) 9:10

Explanation

A : B = 3 : 4

B : C = 6 : 5

Make B the same in both ratios (LCM of 4 and 6 = 12)

A : B = 3 × 3 : 4 × 3 = 9 : 12

B : C = 6 × 2 : 5 × 2 = 12 : 10

So A : B : C = 9 : 12 : 10

A : C = 9 : 10

Hence, A : C = 9 : 10.

Shortcut Method

A/C = (A/B) × (B/C)

= (3/4) × (6/5)

= 18/20

= 9 : 10

Answer: (B) 9:10

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Correct Answer: (D) 3 1/8 %

Explanation

Height last year = 144 cm

Height this year = 148.5 cm

Increase = 148.5 − 144 = 4.5 cm

Percentage change = (Increase / Original height) × 100

= (4.5/144) × 100

= 450/144

= 3.125%

= 3 1/8 %

Hence, her height has increased by 3 1/8 %.

Shortcut Method

1% of 144 = 1.44 cm

3% = 4.32 cm, remaining 4.5 − 4.32 = 0.18 cm

0.18/1.44 = 1/8 %

Total = 3 1/8 %

Answer: (D) 3 1/8 %

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Correct Answer: (C) 20%

Explanation

Marked Price (MP) = Rs. 165

Selling Price (SP) = Rs. 132

Discount = MP − SP

= 165 − 132

= Rs. 33

Discount % = (Discount / MP) × 100

= (33/165) × 100

= 20%

Hence, the discount allowed on the book is 20%.

Shortcut Method

SP/MP = 132/165 = 4/5 = 80%

Discount = 100% − 80%

= 20%

Answer: (C) 20%

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Correct Answer: (C) 53.01

Explanation

Let the required number = x

72.5 − x = 18.76

x = 72.5 − 18.76

= 72.50 − 18.76

= 53.74

Check: 72.5 − 53.74 = 18.76

53.74 is not among the options, so the question has a misprint; the nearest option is 53.01

The printed key shows (D) 74.12, but 74.12 is larger than 72.5, so it cannot be subtracted from 72.5 to leave 18.76

Hence, the correct value is 53.74, and the closest option is (C) 53.01.

Shortcut Method

The number subtracted must be less than 72.5

Options (A) 90.5, (B) 90.76 and (D) 74.12 are all larger than 72.5, so they are rejected

Only (C) 53.01 remains (exact value 72.5 − 18.76 = 53.74)

Answer: (C) 53.01

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Correct Answer: (B) 3%

Explanation

1 hour = 60 minutes = 60 × 60 = 3600 seconds

1 minute 48 seconds = 60 + 48 = 108 seconds

Required % = (108/3600) × 100

= 10800/3600

= 3%

Hence, 1 minute 48 seconds is 3% of 1 hour.

Shortcut Method

1 minute 48 seconds = 1.8 minutes

% of 1 hour = (1.8/60) × 100

= 3%

Answer: (B) 3%

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Correct Answer: (D) 1/12

Explanation

Mean proportional of a and b = √(a × b)

a = 1/4, b = 1/36

Mean proportional = √(1/4 × 1/36)

= √(1/144)

= 1/12

Hence, the mean proportional between 1/4 and 1/36 is 1/12.

Shortcut Method

√(1/4) = 1/2 and √(1/36) = 1/6

Mean proportional = 1/2 × 1/6

= 1/12

Answer: (D) 1/12

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Correct Answer: (C) 15%

Explanation

Old price = Rs. 20 per kg

New price = Rs. 23 per kg

Increase = 23 − 20 = Rs. 3

Percentage increase = (Increase/Old price) × 100

= (3/20) × 100

= 15%

Hence, the price has increased by 15%.

Shortcut Method

Rs. 1 out of Rs. 20 = 5%

Rs. 3 increase = 3 × 5%

= 15%

Answer: (C) 15%

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Correct Answer: (D) Rs. 36

Explanation

Ratio of daily wages = 4 : 3

Let the wages be 4x and 3x

Difference = 4x − 3x = x

x = Rs. 9

First worker’s wage = 4x

= 4 × 9

= Rs. 36

Hence, the daily wage of the first worker is Rs. 36.

Shortcut Method

Difference of ratio terms = 4 − 3 = 1 part

1 part = Rs. 9

First worker = 4 parts = 4 × 9 = Rs. 36

Answer: (D) Rs. 36

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Correct Answer: (D) 90

Explanation

Let Sutapa’s marks = x

Mahua’s marks = x − 10% of x = 90% of x

90% of x = 81

x = (81 × 100)/90

= 8100/90

= 90

Hence, Sutapa got 90 marks.

Shortcut Method

90% → 81

100% → 81 × 100/90

= 90

Answer: (D) 90

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Correct Answer: (B) 3

Explanation

Prime factorisation of 1083:

1083 = 3 × 361

= 3 × 19 × 19

19 is already in a pair; 3 is unpaired

Required multiplier = 3

1083 × 3 = 3249 = 57^2

Hence, 1083 must be multiplied by 3 to make it a perfect square.

Shortcut Method

Digit sum of 1083 = 12, so 1083 is divisible by 3

1083 ÷ 3 = 361 = 19^2 (a perfect square)

So multiply by the leftover factor 3

Answer: (B) 3

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Correct Answer: (C) 20 days

Explanation

(A + B)’s 1 day work = 1/12

B’s 1 day work = 1/30

A’s 1 day work = 1/12 − 1/30

= (5 − 2)/60

= 3/60 = 1/20

Hence, A alone can complete the work in 20 days.

Shortcut Method

A alone = (12 × 30)/(30 − 12)

= 360/18

= 20 days

Answer: (C) 20 days

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Correct Answer: (C) 220

Explanation

Selling Price (SP) = Rs. 180

Loss = 10%

CP = SP × 100/(100 − Loss%)

= 180 × 100/90

= Rs. 200

New SP for 10% profit = CP × (100 + 10)/100

= 200 × 110/100

= Rs. 220

Hence, he should sell it for Rs. 220 to make a profit of 10%.

Shortcut Method

New SP = Old SP × (100 + 10)/(100 − 10)

= 180 × 110/90

= Rs. 220

Answer: (C) 220

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Correct Answer: (C) 432

Explanation

Product of two numbers = HCF × LCM

15552 = 36 × LCM

LCM = 15552/36

= 432

Hence, the LCM of the two numbers is 432.

Shortcut Method

LCM must be a multiple of HCF 36

Check options: only 432 ÷ 36 = 12 exactly

LCM = 432

Answer: (C) 432

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Correct Answer: (B) 15 days

Explanation

Food for 30 children lasts 18 days

Total food = 30 × 18 = 540 child-days

New number of children = 30 + 6 = 36

Days food will last = 540/36

= 15 days

Hence, the food will last for 15 days.

Shortcut Method

M1 × D1 = M2 × D2

30 × 18 = 36 × D2

D2 = 540/36 = 15 days

Answer: (B) 15 days

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Correct Answer: (D) 72 km/h

Explanation

Length of train = 360 m

Time to cross a pole = 18 s

Distance covered = length of train = 360 m

Speed = Distance/Time

= 360/18

= 20 m/s

Speed in km/h = 20 × 18/5

= 72 km/h

Hence, the speed of the train is 72 km/h.

Shortcut Method

Speed (km/h) = (Length/Time) × 18/5

= (360/18) × 18/5

= 360/5 = 72 km/h

Answer: (D) 72 km/h

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Correct Answer: (C) Rs. 64

Explanation

Selling Price (SP) = Rs. 80

Profit = 25%

CP = SP × 100/(100 + Profit%)

= 80 × 100/125

= 8000/125

= Rs. 64

Hence, the cost price of the cloth is Rs. 64.

Shortcut Method

25% = 1/4, so SP = CP + CP/4 = 5/4 of CP

CP = 80 × 4/5

= Rs. 64

Answer: (C) Rs. 64

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Correct Answer: (C) Rs. 756

Explanation

Cost Price (CP) = Rs. 675

Profit = 12% of CP

Profit = (12/100) × 675 = Rs. 81

Selling Price (SP) = CP + Profit

= 675 + 81

= Rs. 756

Hence, the selling price of the radio is Rs. 756.

Shortcut Method

SP = CP × (112/100)

= 675 × 1.12

= Rs. 756

Answer: (C) Rs. 756

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Correct Answer: (C) Rs. 60

Explanation

Let the original price = Rs. x

Increase = 30%

New price = x × (130/100)

x × 130/100 = 78

x = 78 × 100/130

= 7800/130

= Rs. 60

Hence, the price of 1 kg of tea before the increase was Rs. 60.

Shortcut Method

130% → Rs. 78

100% → 78 × 100/130

= Rs. 60

Answer: (C) Rs. 60

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Correct Answer: (B) Book

Explanation

A dialogue is a conversation between characters written down in a text, so among an almirah, a book, a board and a chair it is found only in a book (in plays, novels and stories). This is a simple association question: find the item that contains written conversation.

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Correct Answer: (B) 10

Explanation

Take the terms in pairs: (15, 18), (X, 14), (21, 26), (8, 16). In the first pair the second term exceeds the first by 3 and in the third pair by 5, so the second pair should differ by 4, giving X = 14 − 4 = 10, which matches the printed key (B). The last pair (8, 16) differs by 8 and breaks the pattern, so the series is probably misprinted, but 10 is the only option that fits the 3, 4, 5 progression.

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Correct Answer: (D) 4:3

Explanation

Ram’s time = 15 days, Shyam’s time = 20 days

Earnings are shared in the ratio of work done, i.e. the ratio of one day’s work

Ram’s 1 day’s work = 1/15

Shyam’s 1 day’s work = 1/20

Ratio = 1/15 : 1/20

Multiply both by LCM 60

= 4 : 3

Hence, the ratio of their earnings is 4 : 3.

Shortcut Method

When they work together for the same time, earnings ratio = inverse of time ratio

Time ratio = 15 : 20 = 3 : 4

Earnings ratio = 4 : 3

Answer: (D) 4:3

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Correct Answer: (C) 20%

Explanation

Let the number be x

After 10% decrease, value = 90% of x

(90/100) × x = 54

x = 54 × 100/90

= 60

Required increase = 72 − 60 = 12

Percentage increase = (12/60) × 100

= 20%

Hence, the number must be increased by 20% to become 72.

Shortcut Method

90% = 54, so 10% = 6 and 100% = 60

72 − 60 = 12 = 2 × 6 = 2 × 10%

= 20%

Answer: (C) 20%

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Correct Answer: (B) 435 kg

Explanation

2% = 8.7

1% = 8.7/2 = 4.35

100% = 4.35 × 100

= 435

Hence, 100% = 435, i.e. 435 kg (the units appear only in the options).

Shortcut Method

100% = 2% × 50

= 8.7 × 50

= 435

Answer: (B) 435 kg

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Correct Answer: (C) 2 1/2 years

Explanation

Principal (P) = Rs. 4500

Simple Interest (SI) = Rs. 675

Rate (R) = 6% per annum

Time (T) = (SI × 100)/(P × R)

= (675 × 100)/(4500 × 6)

= 67500/27000

= 2.5 years

Hence, the interest will be Rs. 675 in 2 1/2 years.

Shortcut Method

Interest for 1 year = 6% of 4500 = Rs. 270

T = 675/270

= 2.5 years = 2 1/2 years

Answer: (C) 2 1/2 years

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Correct Answer: (B) Rs. 800

Explanation

Selling Price (SP) = Rs. 720

Loss = 10% of CP

SP = CP × (100 − Loss%)/100

720 = CP × 90/100

CP = 720 × 100/90

= Rs. 800

Hence, the cost price of the article is Rs. 800.

Shortcut Method

10% loss means SP = 9/10 of CP

CP = 720 × 10/9

= Rs. 800

Answer: (B) Rs. 800

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Correct Answer: (B) Rs. 91 7/9

Explanation

Profit = Rs. 14

Profit% = 18%

Profit = 18% of CP

CP = 14 × 100/18

= 700/9

= Rs. 77 7/9

SP = CP + Profit

= 77 7/9 + 14

= Rs. 91 7/9

Hence, the selling price of the article is Rs. 91 7/9.

Shortcut Method

SP = Profit × (100 + Profit%)/Profit%

= 14 × 118/18

= 826/9

= Rs. 91 7/9

Answer: (B) Rs. 91 7/9

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