WBP SI Prelims Mathematics Questions 2021
Q. The average of three numbers is 80. The first number is 10 more than twice the second and the second number is 10 less than thrice the third. What is the lowest number?
(A) 68
(B) 28
(C) 66
(D) 26
Answer & Explanation
Correct Answer: (D) 26
Explanation
Average = 80
Sum of the three numbers = 3 × 80 = 240
Let the third number = c
Second number = 3c − 10
First number = 2 × (3c − 10) + 10 = 6c − 10
(6c − 10) + (3c − 10) + c = 240
10c − 20 = 240
10c = 260
c = 26
Second = 3 × 26 − 10 = 68 and first = 6 × 26 − 10 = 146
Check: 146 + 68 + 26 = 240
Hence, the numbers are 146, 68 and 26, and the lowest number is 26.
Shortcut Method
Total = 6c + 3c + c − 20 = 240
= 10c = 260
= c = 26 (the lowest)
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If the ratio of principal and simple interest at 4% per annum for a specific time is 5 : 2, find the number of years for which the principal was deposited.
(A) 10 years
(B) 15 years
(C) 18 years
(D) 12 years
Answer & Explanation
Correct Answer: (A) 10 years
Explanation
Principal : Simple interest = 5 : 2
Let P = 5k and SI = 2k
SI = (P × R × T) / 100
2k = (5k × 4 × T) / 100
2k = 20kT / 100
2 = T/5
T = 10
Hence, the principal was deposited for 10 years.
Shortcut Method
SI/P = 2/5 = R × T / 100
= 4T/100 = 2/5
= T = 10 years
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A mixture of dettol and water contains 80% of water. What volume of dettol is to be added to 60 litres of this mixture, so that the new mixture contains 75% of water?
(A) 4 litres
(B) 8 litres
(C) 10 litres
(D) 6 litres
Answer & Explanation
Correct Answer: (A) 4 litres
Explanation
Water in 60 litres = 80% of 60 = 48 litres
Dettol in 60 litres = 60 − 48 = 12 litres
Let x litres of dettol be added
New volume = 60 + x
Water remains 48 litres and is 75% of the new mixture
48 = (75/100) × (60 + x)
60 + x = 48 × 4/3 = 64
x = 4
Hence, 4 litres of dettol should be added.
Shortcut Method
New total = 48 ÷ 0.75 = 64 litres
= added dettol = 64 − 60
= 4 litres
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A man standing on the platform finds that an Express train passes him in 15 secs. If the speed of the train is 60 km/hr, what is the length of the train?
(A) 250 meters
(B) 150 meters
(C) 300 meters
(D) 200 meters
Answer & Explanation
Correct Answer: (A) 250 meters
Explanation
Speed = 60 km/hr
= 60 × 5/18 m/s
= 50/3 m/s
Time = 15 seconds
Length of train = Speed × Time
= 50/3 × 15
= 50 × 5
= 250 m
Hence, the length of the train is 250 metres.
Shortcut Method
60 km/hr = 50/3 m/s
= 50/3 × 15
= 250 m
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. M men agreed to purchase an article for Rs. R. If 4 men drop out, how much more (in Rs.) will each have to contribute to purchase the article at the same price?
(A) 4R / (M² − 4M)
(B) 4M / (R² − 4R)
(C) (4M − R) / 4R
(D) (M² − 4R) / MR
Answer & Explanation
Correct Answer: (A) 4R / (M² − 4M)
Explanation
Original share of each man = R/M
Number of men after 4 drop out = M − 4
New share of each man = R/(M − 4)
Extra amount = R/(M − 4) − R/M
= R[M − (M − 4)] / [M(M − 4)]
= R × 4 / [M(M − 4)]
= 4R / (M² − 4M)
Hence, each remaining man pays Rs. 4R/(M² − 4M) more.
Shortcut Method
Extra = R/(M − 4) − R/M
= 4R/[M(M − 4)]
= 4R/(M² − 4M)
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Simplify : (√20 + √1125 − √567)(√500 + √245 + 9√7)
(A) 2012
(B) 1445
(C) 567
(D) 878
Answer & Explanation
Correct Answer: (D) 878
Explanation
√20 = √(4 × 5) = 2√5
√1125 = √(225 × 5) = 15√5
√567 = √(81 × 7) = 9√7
First bracket = 2√5 + 15√5 − 9√7 = 17√5 − 9√7
√500 = √(100 × 5) = 10√5
√245 = √(49 × 5) = 7√5
Second bracket = 10√5 + 7√5 + 9√7 = 17√5 + 9√7
Product = (17√5 − 9√7)(17√5 + 9√7)
= (17√5)² − (9√7)²
= 289 × 5 − 81 × 7
= 1445 − 567
= 878
Hence, the value of the expression is 878.
Shortcut Method
(a − b)(a + b) = a² − b²
= (17√5)² − (9√7)²
= 1445 − 567 = 878
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Find the fourth proportional of the following numbers: 1/3, 1/6, 1/9, ?
(A) 1/18
(B) 1/6
(C) 1/27
(D) 1/3
Answer & Explanation
Correct Answer: (A) 1/18
Explanation
If a, b, c, x are in proportion, a : b = c : x
So x = (b × c) / a
a = 1/3, b = 1/6, c = 1/9
b × c = 1/6 × 1/9 = 1/54
x = (1/54) ÷ (1/3)
x = 1/54 × 3
x = 3/54
x = 1/18
Hence, the fourth proportional is 1/18.
Shortcut Method
x = bc/a
= (1/54) × 3
= 1/18
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. 45 men can produce 10000 electric bulbs in 12 days in a co-operative concern. The concern got an order to produce 10000 electric bulbs in 9 days. How many more men would be employed to meet the order?
(A) 60
(B) 55
(C) 10
(D) 15
Answer & Explanation
Correct Answer: (D) 15
Explanation
Work is the same (10000 bulbs), so men × days is constant
Total work = 45 × 12 = 540 man-days
Men needed for 9 days = 540 ÷ 9
= 60 men
Additional men = 60 − 45
= 15
Hence, 15 more men are needed.
Shortcut Method
45 × 12 = M × 9
= M = 540 ÷ 9 = 60
= 60 − 45 = 15 men
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If time taken to travel between two stations has to be reduced by 20%, then by what per cent would the speed of the train has to be increased?
(A) 25%
(B) 30%
(C) 15%
(D) 20%
Answer & Explanation
Correct Answer: (A) 25%
Explanation
Let the original time = 100 units and speed = s
Distance = speed × time = 100s
New time = 100 − 20 = 80 units
New speed = distance ÷ new time
= 100s ÷ 80
= 1.25s
Increase in speed = 1.25s − s = 0.25s
Percentage increase = 0.25s/s × 100 = 25%
Hence, the speed must be increased by 25%.
Shortcut Method
Time reduced by 20% = 1/5
= speed increase = (1/5) ÷ (1 − 1/5)
= (1/5) ÷ (4/5) = 1/4 = 25%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5,100 more. The sum is
(A) Rs. 1,70,000
(B) Rs. 1,25,000
(C) Rs. 1,20,000
(D) Rs. 1,50,000
Answer & Explanation
Correct Answer: (A) Rs. 1,70,000
Explanation
Let the sum = P and the rate = R%
Extra rate = 1%, time = 3 years
Extra interest = P × 1 × 3 / 100
P × 3 / 100 = 5100
P = 5100 × 100 / 3
P = 1700 × 100
P = 1,70,000
Hence, the sum is Rs. 1,70,000.
Shortcut Method
Extra interest = 3% of P = 5100
= P = 5100 × 100 ÷ 3
= Rs. 1,70,000
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If 3/10th of a road is 45 km, what is the length of 2/5th of that road?
(A) 60 km
(B) 68 km
(C) 26 km
(D) 66 km
Answer & Explanation
Correct Answer: (A) 60 km
Explanation
3/10 of the road = 45 km
Length of the whole road = 45 × 10/3
= 15 × 10
= 150 km
2/5 of the road = 2/5 × 150
= 2 × 30
= 60 km
Hence, 2/5th of the road is 60 km.
Shortcut Method
1/10 of road = 45 ÷ 3 = 15 km
= 2/5 = 4/10 = 4 × 15
= 60 km
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A tea seller blends Tea A worth Rs. 250 per kg with Tea B worth Rs. 150 per kg in a ratio of 2 : 5 and sells the mixed blend at Rs. 200 per kg. What will be his percentage of profit?
(A) 12%
(B) 10%
(C) 18%
(D) 15%
Answer & Explanation
Correct Answer: (A) 12%
Explanation
Take 7 kg of the blend (2 kg of A and 5 kg of B)
Cost of 2 kg of Tea A = 2 × 250 = Rs. 500
Cost of 5 kg of Tea B = 5 × 150 = Rs. 750
Total cost of 7 kg = 500 + 750 = Rs. 1250
Selling price of 7 kg = 7 × 200 = Rs. 1400
Profit = 1400 − 1250 = Rs. 150
Profit % = (150/1250) × 100
= 12%
Hence, the profit is 12%.
Shortcut Method
Cost price of 7 kg = 1250, selling price = 1400
= profit = 150
= 150/1250 × 100 = 12%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Shyam borrowed some money from his friend at simple interest of 6% per annum. He returned his friend Rs. 15,600. After how much time did Shyam return the money if he borrowed Rs. 12,000?
(A) 8 years
(B) 5 years
(C) 3.5 years
(D) 2.5 years
Answer & Explanation
Correct Answer: (B) 5 years
Explanation
Principal = Rs. 12,000
Amount returned = Rs. 15,600
Simple interest = 15,600 − 12,000 = Rs. 3,600
SI = (P × R × T) / 100
3600 = (12000 × 6 × T) / 100
3600 = 720T
T = 3600 ÷ 720
T = 5
Hence, Shyam returned the money after 5 years.
Shortcut Method
Interest per year = 6% of 12000 = Rs. 720
= T = 3600 ÷ 720
= 5 years
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Father is three times as old as his son. After twelve years, his age will be twice as that of the age of his son. What is the present age of the son?
(A) 10 years
(B) 36 years
(C) 14 years
(D) 12 years
Answer & Explanation
Correct Answer: (D) 12 years
Explanation
Let the son’s present age = x years
Father’s present age = 3x years
After 12 years: son = x + 12, father = 3x + 12
3x + 12 = 2(x + 12)
3x + 12 = 2x + 24
3x − 2x = 24 − 12
x = 12
Check: father = 36 now, 48 after 12 years; son = 24 after 12 years; 48 = 2 × 24
Hence, the present age of the son is 12 years.
Shortcut Method
3x + 12 = 2x + 24
= x = 12
= son 12 years (father 36 years)
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. HCF of two numbers is 32 and their LCM is 1760. What is the smaller number?
(A) 160
(B) 152
(C) 102
(D) 110
Answer & Explanation
Correct Answer: (A) 160
Explanation
HCF × LCM = product of the two numbers
Product = 32 × 1760 = 56320
Let the numbers be 32a and 32b, where a and b are co-prime
32a × 32b = 56320
1024ab = 56320
ab = 55
Co-prime pairs with product 55: (1, 55) and (5, 11)
Pair (5, 11) gives numbers 160 and 352
Pair (1, 55) gives numbers 32 and 1760
Only 160 (with 352) appears among the options
Hence, the smaller number is 160 (the pair 32 and 1760 would give 32, which is not an option).
Shortcut Method
ab = 1760 ÷ 32 = 55
= (a, b) = (5, 11)
= numbers 32 × 5 = 160 and 32 × 11 = 352
Note: the pair 32 and 1760 also satisfies the data, but its smaller number 32 is not an option, so 160 is the intended answer.
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. How many two digit prime numbers are there?
(A) 25
(B) 21
(C) Can’t be determined
(D) 23
Answer & Explanation
Correct Answer: (B) 21
Explanation
List the two-digit primes decade by decade
10s: 11, 13, 17, 19 = 4
20s: 23, 29 = 2
30s: 31, 37 = 2
40s: 41, 43, 47 = 3
50s: 53, 59 = 2
60s: 61, 67 = 2
70s: 71, 73, 79 = 3
80s: 83, 89 = 2
90s: 97 = 1
Total = 4 + 2 + 2 + 3 + 2 + 2 + 3 + 2 + 1 = 21
Hence, there are 21 two-digit prime numbers.
Shortcut Method
Primes below 100 = 25
= primes below 10 = 4 (2, 3, 5, 7)
= 25 − 4 = 21
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A began a business with Rs. 2,250 and was joined afterwards by B with Rs. 2,700. If the profits at the end of the year were divided in the ratio of 2 : 1, after how much time B joined the business?
(A) 6 months
(B) 7 months
(C) 3 months
(D) 5 months
Answer & Explanation
Correct Answer: (B) 7 months
Explanation
A invests Rs. 2,250 for 12 months
A’s capital-time = 2250 × 12 = 27000
Let B invest Rs. 2,700 for t months
B’s capital-time = 2700 × t
Profit ratio A : B = 2 : 1
27000 / (2700t) = 2/1
10/t = 2
t = 5
B was in the business for 5 months
B joined after 12 − 5 = 7 months
Hence, B joined the business after 7 months.
Shortcut Method
27000 : 2700t = 2 : 1
= t = 5 months
= joined after 12 − 5 = 7 months
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A sum, at the compound rate of interest, becomes 2½ times in 6 years. The same sum becomes how many times in 18 years?
(A) 5/2
(B) 625/16
(C) 125/8
(D) 25/4
Answer & Explanation
Correct Answer: (C) 125/8
Explanation
Amount after 6 years = 2½ × P = (5/2)P
18 years = 3 periods of 6 years
For compound interest the multiplying factor repeats every 6 years
Amount after 18 years = (5/2) × (5/2) × (5/2) × P
= 125/8 × P
Hence, the sum becomes 125/8 times in 18 years.
Shortcut Method
18 ÷ 6 = 3
= (5/2)³
= 125/8
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A garrison of 500 men had provisions for 24 days. However, a reinforcement of 300 men arrived. The food will now last for
(A) 15 days
(B) 17½ days
(C) 18 days
(D) 16 days
Answer & Explanation
Correct Answer: (A) 15 days
Explanation
Total food = 500 men × 24 days = 12000 man-days
Men after reinforcement = 500 + 300 = 800
Days = 12000 ÷ 800
= 120 ÷ 8
= 15
Hence, the food will last for 15 days.
Shortcut Method
Men and days are inversely proportional
= 500 × 24 = 800 × D
= D = 15 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. At what rate of compound interest per annum, the amount of Rs. 10,000 for 2 years is Rs. 12,100?
(A) 10%
(B) 5%
(C) 11%
(D) 20%
Answer & Explanation
Correct Answer: (A) 10%
Explanation
Principal = Rs. 10,000, Amount = Rs. 12,100, time = 2 years
Amount = P (1 + R/100)²
12100 = 10000 (1 + R/100)²
(1 + R/100)² = 12100/10000
(1 + R/100)² = 121/100
1 + R/100 = 11/10
R/100 = 1/10
R = 10
Hence, the rate of compound interest is 10% per annum.
Shortcut Method
12100/10000 = 1.21 = (1.1)²
= 1 + R/100 = 1.1
= R = 10%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If a person sells an article at a profit of 5%, he gains Rs. 15 more than if he sells it at a loss of 5%. What is the cost price of the article?
(A) Rs. 150
(B) Rs. 120
(C) Rs. 125
(D) Rs. 105
Answer & Explanation
Correct Answer: (A) Rs. 150
Explanation
Let the cost price = C
Selling price at 5% profit = 1.05C
Selling price at 5% loss = 0.95C
Difference = 1.05C − 0.95C = 0.10C
0.10C = 15
C = 15 ÷ 0.10
C = 150
Hence, the cost price of the article is Rs. 150.
Shortcut Method
Difference = 5% + 5% = 10% of C
= 10% of C = 15
= C = Rs. 150
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m², what are the length and breadth of the hall?
(A) 11 m and 6 m
(B) 13 m and 8 m
(C) 14 m and 6 m
(D) 12 m and 7 m
Answer & Explanation
Correct Answer: (D) 12 m and 7 m
Explanation
Let the breadth = x m
Length = (x + 5) m
Area = length × breadth
x(x + 5) = 84
x² + 5x − 84 = 0
x² + 12x − 7x − 84 = 0
(x + 12)(x − 7) = 0
x = 7 (breadth cannot be negative)
Length = 7 + 5 = 12 m
Check: 12 × 7 = 84
Hence, the length is 12 m and the breadth is 7 m.
Shortcut Method
Factors of 84 with difference 5
= 12 × 7 = 84 and 12 − 7 = 5
= length 12 m, breadth 7 m
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The ratio of market prices of wheat and paddy is 2 : 3 and the ratio of quantities consumed in a family is 5 : 4. Find the ratio of expenditure on wheat and paddy.
(A) 6 : 5
(B) 1 : 1
(C) 8 : 15
(D) 5 : 6
Answer & Explanation
Correct Answer: (D) 5 : 6
Explanation
Expenditure = price × quantity
Price ratio wheat : paddy = 2 : 3
Quantity ratio wheat : paddy = 5 : 4
Expenditure on wheat = 2 × 5 = 10 units
Expenditure on paddy = 3 × 4 = 12 units
Ratio = 10 : 12
= 5 : 6
Hence, the ratio of expenditure on wheat and paddy is 5 : 6.
Shortcut Method
(2 × 5) : (3 × 4)
= 10 : 12
= 5 : 6
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If a seller sold two sarees at Rs. 400 each and made a profit of 20% on the first and a loss of 20% on the second, what is his total profit or loss on the whole?
(A) No profit no loss
(B) 4% profit
(C) 1% profit
(D) 4% loss
Answer & Explanation
Correct Answer: (D) 4% loss
Explanation
First saree: SP = 400 at 20% profit
CP of first = 400 × 100/120 = Rs. 333.33
Second saree: SP = 400 at 20% loss
CP of second = 400 × 100/80 = Rs. 500
Total CP = 333.33 + 500 = Rs. 833.33
Total SP = 400 + 400 = Rs. 800
Loss = 833.33 − 800 = Rs. 33.33
Loss % = 33.33/833.33 × 100 = 4%
Hence, the seller makes a loss of 4% on the whole.
Shortcut Method
Equal selling prices with equal profit and loss % always give a loss
= loss % = (20 × 20)/100
= 4% loss
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A and B can do a piece of work in 10 and 15 days respectively. A alone did the work for 4 days and then B did it for 5 days. Thereafter C did the remaining work in 8 days. How long will they take to complete the work together?
(A) 5 days
(B) 8 days
(C) 3 days
(D) 7 days
Answer & Explanation
Correct Answer: (A) 5 days
Explanation
Total work = LCM of 10 and 15 = 30 units
A’s 1 day work = 30 ÷ 10 = 3 units
B’s 1 day work = 30 ÷ 15 = 2 units
Work done by A in 4 days = 4 × 3 = 12 units
Work done by B in 5 days = 5 × 2 = 10 units
Remaining work = 30 − 12 − 10 = 8 units
C does 8 units in 8 days, so C’s 1 day work = 1 unit
A + B + C together in 1 day = 3 + 2 + 1 = 6 units
Time together = 30 ÷ 6 = 5 days
Hence, A, B and C together will take 5 days.
Shortcut Method
A + B + C = 3 + 2 + 1 = 6 units per day
= 30 ÷ 6
= 5 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Which least number is divisible by 12, 15, 20 and 25?
(A) 300
(B) 150
(C) 600
(D) 200
Answer & Explanation
Correct Answer: (A) 300
Explanation
The least such number is the LCM of 12, 15, 20 and 25
12 = 2² × 3
15 = 3 × 5
20 = 2² × 5
25 = 5²
LCM = 2² × 3 × 5²
= 4 × 3 × 25
= 300
Hence, the least number is 300.
Shortcut Method
LCM takes the highest power of each prime
= 2² × 3 × 5²
= 300
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
WBP SI Prelims Mathematics Questions 2019
Q. Father is four times the age of his daughter. If after 5 years, he would be three times of daughter’s age, then further after 5 years, how many times he would be of daughter’s age?
(A) 2 times
(B) 3 times
(C) 1.5 times
(D) 2.5 times
Answer & Explanation
Correct Answer: (D) 2.5 times
Explanation
Let the daughter’s present age = x years
Father’s present age = 4x years
After 5 years: father = 4x + 5, daughter = x + 5
4x + 5 = 3(x + 5)
4x + 5 = 3x + 15
x = 10
Daughter’s present age = 10 years, father’s present age = 40 years
After 5 + 5 = 10 years: father = 50 years, daughter = 20 years
Ratio = 50 ÷ 20 = 2.5
Hence, the father will be 2.5 times the daughter’s age.
Shortcut Method
4x + 5 = 3x + 15, so x = 10
= ages after 10 years: 50 and 20
= 50 ÷ 20 = 2.5 times
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is
(A) 24
(B) 81
(C) 18
(D) 32
Answer & Explanation
Correct Answer: (A) 24
Explanation
Let the digits be x (tens) and y (units)
Product of digits: xy = 8
Possible numbers with digit product 8: 18, 81, 24, 42
Number = 10x + y, reversed number = 10y + x
(10y + x) − (10x + y) = 18
9(y − x) = 18
y − x = 2
Pairs with xy = 8: (1, 8) gives difference 7, (2, 4) gives difference 2
So x = 2 and y = 4
Hence, the number is 24 (check: 24 + 18 = 42).
Shortcut Method
Number + 18 = reversed number
= digits differ by 18 ÷ 9 = 2
= the pair with product 8 and difference 2 is 2, 4
= number 24 (24 + 18 = 42)
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Find the value of 0.002 × 0.5 = ?
(A) 0.001
(B) 0.1
(C) 0.0001
(D) 0.01
Answer & Explanation
Correct Answer: (A) 0.001
Explanation
0.002 = 2/1000
0.5 = 5/10
0.002 × 0.5 = (2/1000) × (5/10)
= 10/10000
= 1/1000
= 0.001
Hence, 0.002 × 0.5 = 0.001.
Shortcut Method
2 × 5 = 10
= decimal places: 3 + 1 = 4
= 10 with 4 places = 0.0010 = 0.001
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The respective ratio between 52% of X and 30% of Y is 12 : 5. If X is 50 more than Y, what is the value of ‘2X + Y’ ?
(A) 260
(B) 490
(C) 230
(D) 390
Answer & Explanation
Correct Answer: (B) 490
Explanation
52% of X : 30% of Y = 12 : 5
0.52X / 0.30Y = 12/5
X/Y = (12 × 0.30) / (5 × 0.52)
X/Y = 3.6/2.6 = 18/13
Let X = 18k and Y = 13k
X − Y = 50
5k = 50
k = 10
X = 180 and Y = 130
2X + Y = 2 × 180 + 130 = 360 + 130 = 490
Hence, the value of 2X + Y is 490.
Shortcut Method
X : Y = 18 : 13 (difference 5 parts = 50)
= 1 part = 10, so X = 180, Y = 130
= 2X + Y = 360 + 130 = 490
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Amit is 6 yrs. older than his wife Soma. The present age of their son, Bunny is 1/3rd of Soma’s present age. If the sum of present age of Amit and Bunny is 54 yrs., what was Soma’s age when Bunny was born ?
(A) 28
(B) 36
(C) 24
(D) 32
Answer & Explanation
Correct Answer: (C) 24
Explanation
Let Soma’s present age = x years
Amit’s present age = x + 6
Bunny’s present age = x/3
(x + 6) + x/3 = 54
3x + 18 + x = 162
4x = 144
x = 36
Soma = 36 years, Amit = 42 years, Bunny = 36/3 = 12 years
Bunny was born 12 years ago
Soma’s age at that time = 36 − 12 = 24 years
Hence, Soma was 24 years old when Bunny was born.
Shortcut Method
Amit + Bunny = (x + 6) + x/3 = 54
= 4x/3 = 48, x = 36
= Soma’s age at Bunny’s birth = 36 − 36/3 = 24
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The sum of 3 numbers is 136. If the ratios between first and second be 2:3 and that between second and third is 5:3, then the second number is
(A) 48
(B) 60
(C) 40
(D) 52
Answer & Explanation
Correct Answer: (B) 60
Explanation
First : second = 2 : 3 = 10 : 15 (multiply by 5)
Second : third = 5 : 3 = 15 : 9 (multiply by 3)
First : second : third = 10 : 15 : 9
Sum of ratios = 10 + 15 + 9 = 34
1 part = 136 ÷ 34 = 4
Second number = 15 × 4 = 60
Hence, the second number is 60.
Shortcut Method
Ratio 10 : 15 : 9, total 34 parts
= 136 ÷ 34 = 4
= 15 × 4 = 60
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would 21 women take, if 3 women do as much work as 2 men ?
(A) 20
(B) 30
(C) 18
(D) 25
Answer & Explanation
Correct Answer: (B) 30
Explanation
Total work = 15 men × 21 days × 8 hrs = 2520 man-hours
3 women = 2 men
1 woman = 2/3 man
21 women = 21 × 2/3 = 14 men
Work = 14 × D × 6 = 2520
84D = 2520
D = 2520 ÷ 84 = 30
Hence, 21 women will take 30 days.
Shortcut Method
21 women = 14 men
= 15 × 21 × 8 = 14 × D × 6
= D = (15 × 21 × 8) / (14 × 6) = 30 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. How many seconds a train 100 meters in length running at the rate of 36 km/hr will take to pass a certain telegraph post ?
(A) 12 seconds
(B) 18 seconds
(C) 10 seconds
(D) 15 seconds
Answer & Explanation
Correct Answer: (C) 10 seconds
Explanation
Distance to be covered = length of train = 100 m
Speed = 36 km/hr
= 36 × 5/18 m/s
= 10 m/s
Time = Distance ÷ Speed
= 100 ÷ 10
= 10 seconds
Hence, the train takes 10 seconds to pass the post.
Shortcut Method
36 km/hr = 10 m/s
= time = 100 ÷ 10
= 10 seconds
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. ‘A’ can complete a piece of work in 12 days. ‘A’ and ‘B’ together can complete the same piece of work in 8 days. How many days can ‘B’ alone complete the same piece of work ?
(A) 18 days
(B) 28 days
(C) 15 days
(D) 24 days
Answer & Explanation
Correct Answer: (D) 24 days
Explanation
Total work = LCM of 12 and 8 = 24 units
A’s 1 day work = 24 ÷ 12 = 2 units
(A + B)’s 1 day work = 24 ÷ 8 = 3 units
B’s 1 day work = 3 − 2 = 1 unit
B’s time = 24 ÷ 1 = 24 days
Hence, B alone can complete the work in 24 days.
Shortcut Method
B = 1/8 − 1/12
= (3 − 2)/24
= 1/24, so 24 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The sum of two digits of a two digit number is 12 and the difference between the two digits of the two digit number is 6. What is the two digit number ?
(A) 75
(B) 93
(C) 60
(D) 84
Answer & Explanation
Correct Answer: (B) 93
Explanation
Let the digits be x and y
x + y = 12
x − y = 6
Adding: 2x = 18
x = 9
y = 12 − 9 = 3
The digits are 9 and 3
Numbers formed: 93 and 39; only 93 is in the options
Check: 9 + 3 = 12 and 9 − 3 = 6
Hence, the two-digit number is 93.
Shortcut Method
Bigger digit = (12 + 6) ÷ 2 = 9
= smaller digit = (12 − 6) ÷ 2 = 3
= number 93 (39 is not an option)
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. Starting together, how many times will the bells toll together in a span of 1 hour?
(A) 8
(B) 12
(C) 5
(D) 10
Answer & Explanation
Correct Answer: (D) 10
Explanation
The bells toll together again after the LCM of 9, 6, 4, 10 and 8 seconds
9 = 3², 6 = 2 × 3, 4 = 2², 10 = 2 × 5, 8 = 2³
LCM = 2³ × 3² × 5 = 360 seconds
1 hour = 60 × 60 = 3600 seconds
Number of times they toll together again = 3600 ÷ 360 = 10
So 10 more times after the first start together
Hence, the bells toll together 10 times in 1 hour after the start.
Shortcut Method
LCM = 360 s
= 3600 ÷ 360 = 10
Note: if the toll at the very start is also counted the total is 11, but 11 is not an option, so 10 (D) is the only workable answer.
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Sachin Tendulkar has a certain average for 11 innings. In the 12th innings he scores 120 runs and there by increases his average by 5 runs, his new average is
(A) 62
(B) 66
(C) 60
(D) 65
Answer & Explanation
Correct Answer: (D) 65
Explanation
Let the average of 11 innings = x
Total runs in 11 innings = 11x
Total runs after 12 innings = 11x + 120
New average = x + 5
11x + 120 = 12(x + 5)
11x + 120 = 12x + 60
x = 60
New average = 60 + 5 = 65
Hence, his new average is 65.
Shortcut Method
12th score = old average + 12 × 5
= 120 = x + 60
= x = 60, new average = 60 + 5 = 65
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The wheel of a motor car makes 1000 revolutions in moving 440 m. The diameter (in meter) of the wheel is
(A) 0.34
(B) 0.14
(C) 0.44
(D) 0.24
Answer & Explanation
Correct Answer: (B) 0.14
Explanation
Distance in 1 revolution = circumference = 440 ÷ 1000 = 0.44 m
Circumference = πd
πd = 0.44
d = 0.44 ÷ (22/7)
d = 0.44 × 7/22
d = 3.08/22
d = 0.14 m
Hence, the diameter of the wheel is 0.14 m.
Shortcut Method
0.44 ÷ π, with π = 22/7
= 0.44 × 7/22
= 0.02 × 7 = 0.14 m
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
(A) 10
(B) 16
(C) 9
(D) 15
Answer & Explanation
Correct Answer: (B) 16
Explanation
The bells toll together again after the LCM of 2, 4, 6, 8, 10 and 12 seconds
2 = 2, 4 = 2², 6 = 2 × 3, 8 = 2³, 10 = 2 × 5, 12 = 2² × 3
LCM = 2³ × 3 × 5 = 120 seconds
30 minutes = 30 × 60 = 1800 seconds
1800 ÷ 120 = 15 times after the start
The bells commence tolling together at the start, so that toll is also counted
Total number of times = 15 + 1 = 16
Hence, the bells toll together 16 times in 30 minutes.
Shortcut Method
LCM = 120 s, 30 min = 1800 s
= 1800 ÷ 120 = 15
= 15 + 1 (the first toll) = 16
Note: the question says the bells “commence tolling together”, so the first toll is counted and the answer is 16. If the first toll were left out the answer would be 15, which is option (D).
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The difference between the areas of a rectangle and square is 35 cm². If the rectangle’s length and breadth are 50% more and 10% less respectively than the side of the square, what is the area of the rectangle? (in cm²)
(A) 105
(B) 145
(C) 100
(D) 135
Answer & Explanation
Correct Answer: (D) 135
Explanation
Let the side of the square = a cm
Area of square = a²
Length of rectangle = a × 150/100 = 1.5a
Breadth of rectangle = a × 90/100 = 0.9a
Area of rectangle = 1.5a × 0.9a = 1.35a²
Difference = 1.35a² − a² = 0.35a²
0.35a² = 35
a² = 100
Area of rectangle = 1.35 × 100 = 135 cm²
Hence, the area of the rectangle is 135 cm².
Shortcut Method
Rectangle area = 1.5 × 0.9 = 1.35 times the square
= extra area = 0.35 times the square = 35
= square = 100, rectangle = 135 cm²
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A man goes uphill at an average speed of 24 kmph. and comes down at an average speed of 30 kmph., the distance travelled in the both the cases being the same. The average speed for the entire journey is
(A) 30 kmph.
(B) 30.8 kmph.
(C) 26.6 kmph.
(D) 32.6 kmph.
Answer & Explanation
Correct Answer: (C) 26.6 kmph.
Explanation
Distance is the same for both journeys, so use the harmonic mean
Average speed = 2xy/(x + y)
= (2 × 24 × 30)/(24 + 30)
= 1440/54
= 80/3
= 26.66… kmph
≈ 26.6 kmph (the nearest option; 26.67 would round to 26.7)
Hence, the average speed is about 26.6 kmph.
Shortcut Method
2 × 24 × 30 ÷ 54
= 1440 ÷ 54
= 26.67 kmph (option (C) 26.6, the nearest)
Note: the exact value is 26.67 kmph; option (C) gives it truncated to one decimal place.
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The average weight of a group of 75 girls was calculated as 47 kg. It was later discovered that the weight of one of the girls was read as 45 kg, whereas her actual was 25 kg. What is the actual average weight of the group of 75 girls ? (rounded off to two digits after decimal)
(A) 46.73 kg.
(B) 45.96 kg.
(C) 47.26 kg.
(D) 46.64 kg.
Answer & Explanation
Correct Answer: (A) 46.73 kg.
Explanation
Wrong total weight = 75 × 47 = 3525 kg
Wrong reading = 45 kg and actual weight = 25 kg
Excess in total = 45 − 25 = 20 kg
Correct total weight = 3525 − 20 = 3505 kg
Correct average = 3505 ÷ 75
= 46.7333…
= 46.73 kg (to two decimals)
Hence, the actual average weight is 46.73 kg.
Shortcut Method
Average falls by 20 ÷ 75 = 0.2667
= 47 − 0.2667
= 46.7333 = 46.73 kg
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. In a relief camp of 550 men, food was enough for 28 days. If 150 more people joined the camp, the same amount of food will be enough for
(A) 25 days
(B) 10 days
(C) 35 days
(D) 22 days
Answer & Explanation
Correct Answer: (D) 22 days
Explanation
Total food = 550 men × 28 days = 15400 man-days
New number of men = 550 + 150 = 700
Days = 15400 ÷ 700
= 154 ÷ 7
= 22
Hence, the food will last for 22 days.
Shortcut Method
Men and days are inversely proportional
= 550 × 28 = 700 × D
= D = 15400 ÷ 700 = 22 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
(A) 200
(B) 195
(C) 170
(D) 220
Answer & Explanation
Correct Answer: (B) 195
Explanation
Cloth woven in 1 second = 0.128 m
Time = Total cloth ÷ Cloth per second
= 25 ÷ 0.128
= 25000 ÷ 128
= 195.31…
≈ 195 seconds
Hence, the loom takes approximately 195 seconds.
Shortcut Method
0.128 × 195 = 24.96 ≈ 25
= 25 ÷ 0.128 = 195.3
= about 195 s
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. In an election between two candidates, 75% of the voters cast their votes, out of which 02% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of voters.
(A) 15800
(B) 16800
(C) 15700
(D) 16700
Answer & Explanation
Correct Answer: (B) 16800
Explanation
Let the total number of voters = N
Votes cast = 75% of N = 0.75N
Valid votes = 98% of 0.75N = 0.98 × 0.75N = 0.735N
75% of valid votes = 9261
0.75 × 0.735N = 9261
0.55125N = 9261
N = 9261 ÷ 0.55125
N = 16800
Hence, the total number of voters is 16800.
Shortcut Method
Valid votes = 9261 × 100/75 = 12348
= votes cast = 12348 × 100/98 = 12600
= total voters = 12600 × 100/75 = 16800
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A sum of money doubles itself in 4 years at a simple interest. In how many years will it amount to 8 times of itself ?
(A) 12 years
(B) 28 years
(C) 8 years
(D) 24 years
Answer & Explanation
Correct Answer: (B) 28 years
Explanation
Let the principal = P
Amount after 4 years = 2P
Simple interest in 4 years = 2P − P = P
Interest per year = P ÷ 4 = P/4
For amount 8P, interest needed = 8P − P = 7P
Time = 7P ÷ (P/4)
= 7 × 4
= 28 years
Hence, the sum becomes 8 times in 28 years.
Shortcut Method
Doubles in 4 years, so rate = 100/4 = 25% p.a.
= time for 8 times = (8 − 1) × 100/25
= 7 × 4 = 28 years
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A man purchased 35 kg of rice at the rate of Rs. 9.50 per kg and 30 kg at the rate of Rs. 10.50 per kg. He mixed the two. Approximately, at what price (in Rs.) per kg should he sell the mixture to make 35% profit in the transaction ?
(A) 12.50
(B) 13.50
(C) 12
(D) 13
Answer & Explanation
Correct Answer: (B) 13.50
Explanation
Cost of 35 kg = 35 × 9.50 = Rs. 332.50
Cost of 30 kg = 30 × 10.50 = Rs. 315
Total cost = 332.50 + 315 = Rs. 647.50
Total quantity = 35 + 30 = 65 kg
Selling price for 35% profit = 647.50 × 135/100
= Rs. 874.125
Selling price per kg = 874.125 ÷ 65
= Rs. 13.4481
≈ Rs. 13.50
Hence, the mixture should be sold at about Rs. 13.50 per kg.
Shortcut Method
Cost per kg = 647.50 ÷ 65 = 9.96
= selling price = 9.96 × 1.35
= 13.45, nearest option Rs. 13.50
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The ratio of the length and the breadth of a rectangular plot is 6:5 respectively. If the breadth of the plot is 34 meters less than the length, what is the perimeter of the rectangular plot ?
(A) 408 meters
(B) 814 meters
(C) 374 meters
(D) 748 meters
Answer & Explanation
Correct Answer: (D) 748 meters
Explanation
Length : breadth = 6 : 5
Let length = 6x and breadth = 5x
Length − breadth = 34
6x − 5x = 34
x = 34
Length = 6 × 34 = 204 m
Breadth = 5 × 34 = 170 m
Perimeter = 2 × (204 + 170)
= 2 × 374
= 748 m
Hence, the perimeter of the plot is 748 m.
Shortcut Method
1 part of the ratio = 34 m
= length + breadth = 11 parts = 11 × 34 = 374
= perimeter = 2 × 374 = 748 m
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. In an examination it is required to get 40% of the aggregate marks to pass. A student gets 265 marks and is declared failed by 55 marks. What is the total marks in the said examination?
(A) 750
(B) 550
(C) 800
(D) 650
Answer & Explanation
Correct Answer: (C) 800
Explanation
Passing marks = marks obtained + shortfall
= 265 + 55
= 320
40% of total marks = 320
Total marks = 320 × 100/40
= 320 × 2.5
= 800
Hence, the total marks in the examination are 800.
Shortcut Method
Pass marks = 265 + 55 = 320
= 320 ÷ 0.40
= 800
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. If the new numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35. What is the original fraction?
(A) 3/14
(B) 2/15
(C) 3/16
(D) 3/10
Answer & Explanation
Correct Answer: (A) 3/14
Explanation
Let the original fraction = x/y
New numerator = x + 200% of x = 3x
New denominator = y + 150% of y = 2.5y
3x/(2.5y) = 9/35
x/y = (9/35) × (2.5/3)
x/y = 22.5/105
x/y = 3/14
Hence, the original fraction is 3/14.
Shortcut Method
New fraction = (3/2.5) × original
= original = (9/35) × (2.5/3)
= 7.5/35 = 3/14
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
WBP SI Prelims Mathematics Questions 2018
Q. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 20, 35, 45
(B) 16, 28, 36
(C) 8, 20, 28
(D) 8, 14, 18
Answer & Explanation
Correct Answer: (B) 16, 28, 36
Explanation
Ratio of present ages = 4 : 7 : 9
Let the present ages be 4x, 7x and 9x
Sum of present ages = 4x + 7x + 9x = 20x
Sum of ages 8 years ago = 20x − (3 × 8) = 20x − 24
20x − 24 = 56
20x = 80
x = 4
Ages = 4 × 4, 7 × 4, 9 × 4 = 16, 28, 36
Hence, the present ages are 16, 28 and 36 years.
Shortcut Method
Present sum = 56 + 24 = 80
= 80 ÷ 20 = 4 (value of 1 ratio unit)
= 16, 28, 36
Check: 16 + 28 + 36 = 80
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. ‘A’ can do a work in 10 days, ‘B’ in 12 days and ‘C’ in 15 days. They started doing work together but after 2 days of starting of work, ‘A’ left and 4 days before completion, ‘C’ left the work. In how many days work was finished?
(A) 65/7 days
(B) 67/9 days
(C) 64/9 days
(D) 66/8 days
Answer & Explanation
Correct Answer: (C) 64/9 days
Explanation
Total work = LCM of 10, 12, 15 = 60 units
A’s 1 day work = 60 ÷ 10 = 6 units
B’s 1 day work = 60 ÷ 12 = 5 units
C’s 1 day work = 60 ÷ 15 = 4 units
Let the work finish in T days
A works for 2 days = 6 × 2 = 12 units
B works for T days = 5T units
C works for (T − 4) days = 4(T − 4) units
12 + 5T + 4(T − 4) = 60
12 + 5T + 4T − 16 = 60
9T = 64
T = 64/9 days
Hence, the work was finished in 64/9 days.
Shortcut Method
Work done = 6×2 + 5T + 4(T − 4) = 60
= 9T − 4 = 60
= T = 64/9 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. How much time will take by a 100 metre long train, moving at a speed of 30 km/hr, to pass a man standing at a station?
(A) 14 sec.
(B) 12 sec.
(C) 10 sec.
(D) 16 sec.
Answer & Explanation
Correct Answer: (B) 12 sec.
Explanation
Distance to be covered = length of train = 100 m
Speed = 30 km/hr
= 30 × (5/18) m/s
= 25/3 m/s
Time = Distance ÷ Speed
= 100 ÷ (25/3)
= 100 × 3/25
= 12 seconds
Hence, the train passes the man in 12 seconds.
Shortcut Method
Time = (Length × 18)/(Speed × 5)
= (100 × 18)/(30 × 5)
= 1800/150
= 12 s
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 4 hrs.
(B) 3 hrs. 45 mins.
(C) 3 hrs. 15 mins.
(D) 4 hrs. 15 mins.
Answer & Explanation
Correct Answer: (B) 3 hrs. 45 mins.
Explanation
1 tap fills the full tank in 6 hours
Time to fill half the tank = 6 ÷ 2 = 3 hours
Now 1 + 3 = 4 taps work together
Rate of 4 taps = 4 × (1/6) = 2/3 tank per hour
Remaining work = 1/2 tank
Time = (1/2) ÷ (2/3)
= 3/4 hour
= 45 minutes
Total time = 3 hours + 45 minutes
Hence, the tank is completely filled in 3 hours 45 minutes.
Shortcut Method
4 taps fill half the tank in = 3/4 hour
= 6/(2 × 4) = 0.75 h
= 45 minutes
Total = 3 h 45 min
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can finish it in 8 days. Number of days taken by 2 men and 1 boy to finish it will be:-
(A) 12 1/2 days
(B) 13 days
(C) 13 1/2 days
(D) 14 days
Answer & Explanation
Correct Answer: (A) 12 1/2 days
Explanation
Let 1 day work of 1 man = m and of 1 boy = b
2m + 3b = 1/10 … (i)
3m + 2b = 1/8 … (ii)
Adding (i) and (ii): 5m + 5b = 1/10 + 1/8 = 9/40
m + b = 9/200
Subtracting (i) from (ii): m − b = 1/8 − 1/10 = 1/40 = 5/200
m = (9/200 + 5/200)/2 = 7/200
b = (9/200 − 5/200)/2 = 2/200
2m + b = 14/200 + 2/200 = 16/200 = 2/25
Days = 25/2 = 12 1/2
Hence, 2 men and 1 boy finish the work in 12 1/2 days.
Shortcut Method
Take total work = 40 units
2m + 3b = 4 and 3m + 2b = 5
= m = 1.4, b = 0.4
= 2m + b = 3.2 units per day
= 40 ÷ 3.2 = 12.5 days
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The HCF and LCM of two different numbers both greater than 13, are 13 and 273 respectively. Then the sum of the numbers is:-
(A) 290
(B) 288
(C) 286
(D) 130
Answer & Explanation
Correct Answer: (D) 130
Explanation
HCF = 13, LCM = 273
Let the numbers be 13a and 13b, where a and b are co-prime
a × b = LCM ÷ HCF = 273 ÷ 13 = 21
Co-prime pairs with product 21 = (1, 21) and (3, 7)
(1, 21) gives 13 and 273, but 13 is not greater than 13
(3, 7) gives 39 and 91
Sum = 39 + 91 = 130
Hence, the sum of the numbers is 130.
Shortcut Method
Sum = 13 × (3 + 7)
= 13 × 10
= 130
Check: 39 × 91 = 3549 = 13 × 273
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg was:-
(A) Rs. 175.50
(B) Rs. 170
(C) Rs. 169.50
(D) Rs. 180
Answer & Explanation
Correct Answer: (A) Rs. 175.50
Explanation
Let the price of the third variety = Rs. x per kg
Quantities in the ratio 1 : 1 : 2 (total 4 parts)
Mean price = (126 × 1 + 135 × 1 + x × 2)/4
(261 + 2x)/4 = 153
261 + 2x = 612
2x = 351
x = Rs. 175.50
Hence, the third variety costs Rs. 175.50 per kg.
Shortcut Method
Shortfall of the two cheaper teas = (153 − 126) + (153 − 135)
= 27 + 18 = 45
= 2 × (x − 153) = 45
= x = 153 + 22.5 = Rs. 175.50
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. In an examination 17% of the candidates failed in Bengali and 18% in English. If 5% failed in both Bengali and English, the percentage of those who passed in both the subjects is:-
(A) 30%
(B) 40%
(C) 60%
(D) 70%
Answer & Explanation
Correct Answer: (D) 70%
Explanation
Failed in Bengali = 17%
Failed in English = 18%
Failed in both = 5%
Failed in at least one = 17 + 18 − 5 = 30%
Passed in both = 100 − 30
= 70%
Hence, 70% of the candidates passed in both subjects.
Shortcut Method
Passed in both = 100 − (17 + 18 − 5)
= 100 − 30
= 70%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. On dividing 43628 by a certain number the quotient and the remainder were 76 and 536 respectively. Find the divisor.
(A) 536
(B) 567
(C) 765
(D) 576
Answer & Explanation
Correct Answer: (B) 567
Explanation
Dividend = Divisor × Quotient + Remainder
43628 = Divisor × 76 + 536
Divisor × 76 = 43628 − 536
= 43092
Divisor = 43092 ÷ 76
= 567
Check: remainder 536 is less than divisor 567
Hence, the divisor is 567.
Shortcut Method
Option check: 567 × 76 = 567 × 70 + 567 × 6
= 39690 + 3402
= 43092
= 43092 + 536 = 43628
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Find the length of the bridge, which a train 130 metre long and travelling at 45 km/hr can cross in 30 seconds.
(A) 245 metre
(B) 225 metre
(C) 200 metre
(D) 250 metre
Answer & Explanation
Correct Answer: (A) 245 metre
Explanation
Speed = 45 km/hr
= 45 × (5/18) m/s
= 12.5 m/s
Distance covered in 30 s = 12.5 × 30
= 375 m
Distance = Length of train + Length of bridge
375 = 130 + Length of bridge
Length of bridge = 375 − 130
= 245 m
Hence, the length of the bridge is 245 metres.
Shortcut Method
Total distance = 12.5 × 30
= 375 m
= 375 − 130
= 245 m
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A sum of money triples itself, the rate of simple interest being 5% per annum. What is the time period?
(A) 40 years
(B) 30 years
(C) 20 years
(D) 60 years
Answer & Explanation
Correct Answer: (A) 40 years
Explanation
Let Principal = P
Amount = 3P
Simple Interest (SI) = 3P − P = 2P
SI = (P × R × T)/100
2P = (P × 5 × T)/100
T = (2 × 100)/5
= 40 years
Hence, the money triples itself in 40 years.
Shortcut Method
To become n times, T = (n − 1) × 100/R
= (3 − 1) × 100/5
= 200/5
= 40 years
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, then what is the percentage of students who do not get scholarship?
(A) 75%
(B) 72%
(C) 50%
(D) 76%
Answer & Explanation
Correct Answer: (D) 76%
Explanation
Boys : Girls = 3 : 2
Let boys = 3k and girls = 2k, total = 5k
Boys with scholarship = 20% of 3k = 0.6k
Girls with scholarship = 30% of 2k = 0.6k
Total with scholarship = 0.6k + 0.6k = 1.2k
Percentage with scholarship = (1.2k/5k) × 100 = 24%
Percentage without scholarship = 100 − 24
= 76%
Hence, 76% of the students do not get a scholarship.
Shortcut Method
Weighted average = (3 × 20 + 2 × 30)/(3 + 2)
= 120/5
= 24%
= 100 − 24 = 76%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The sum of two numbers are 25 and their difference is 13. Find their product.
(A) 315
(B) 114
(C) 104
(D) 325
Answer & Explanation
Correct Answer: (B) 114
Explanation
Let the numbers be x and y
x + y = 25
x − y = 13
Adding: 2x = 38
x = 19
y = 25 − 19 = 6
Product = 19 × 6
= 114
Hence, the product of the two numbers is 114.
Shortcut Method
xy = [(x + y)² − (x − y)²]/4
= (25² − 13²)/4
= (625 − 169)/4
= 456/4
= 114
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.75
(B) 6.5
(C) 6.25
(D) 7
Answer & Explanation
Correct Answer: (C) 6.25
Explanation
Runs in first 10 overs = 10 × 3.2
= 32 runs
Runs needed in remaining 40 overs = 282 − 32
= 250 runs
Required run rate = 250 ÷ 40
= 6.25
Hence, the required run rate is 6.25 runs per over.
Shortcut Method
Remaining runs = 282 − 32 = 250
= 250/40
= 25/4 = 6.25
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The average of three numbers is 77. The first number is twice of the second one and second number is twice of the third number. Find the three numbers.
(A) 44, 22, 11
(B) 88, 44, 22
(C) 40, 20, 10
(D) 133, 66, 33
Answer & Explanation
Correct Answer: (D) 133, 66, 33
Explanation
Average = 77
Sum of the three numbers = 3 × 77 = 231
Let the third number = c
Second number = 2c
First number = 2 × 2c = 4c
4c + 2c + c = 231
7c = 231
c = 33
Second = 66, first = 132
Hence, the numbers are 132, 66 and 33.
Shortcut Method
Ratio = 4 : 2 : 1 (7 parts)
= 231 ÷ 7 = 33
= 132, 66, 33
Note: option (D) is printed as 133, 66, 33. This is a misprint for 132, 66, 33 (sum 231), so (D) is the intended answer; no option gives the exact numbers.
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The cost price of a sewing machine is Rs. 800. The shopkeeper allows successive discounts on 15% and 10%. What is the selling price of the sewing machine?
(A) Rs. 720
(B) Rs. 680
(C) Rs. 600
(D) Rs. 612
Answer & Explanation
Correct Answer: (D) Rs. 612
Explanation
Marked price = Rs. 800
Price after first discount of 15% = 800 × (85/100)
= Rs. 680
Price after second discount of 10% = 680 × (90/100)
= Rs. 612
Hence, the selling price is Rs. 612.
Shortcut Method
Net discount = 15 + 10 − (15 × 10)/100
= 25 − 1.5 = 23.5%
= 800 × (76.5/100)
= Rs. 612
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
(A) 8 : 3
(B) 3 : 2
(C) 3 : 1
(D) Cannot be determined
Answer & Explanation
Correct Answer: (A) 8 : 3
Explanation
Upstream time = 8 h 48 min = 8 4/5 h = 44/5 h
Downstream time = 4 h
For the same distance, speed is inversely proportional to time
Upstream speed : Downstream speed = 4 : 44/5 = 20 : 44 = 5 : 11
Let upstream speed = 5k and downstream speed = 11k
Speed of boat = (11k + 5k)/2 = 8k
Speed of current = (11k − 5k)/2 = 3k
Boat : Current = 8k : 3k
Hence, the ratio is 8 : 3.
Shortcut Method
Boat : Current = (T1 + T2) : (T1 − T2)
= (8.8 + 4) : (8.8 − 4)
= 12.8 : 4.8
= 8 : 3
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A number is doubled and 9 is added. If resultant is trebled it becomes 75. What is that number?
(A) 12
(B) 10
(C) 8
(D) 14
Answer & Explanation
Correct Answer: (C) 8
Explanation
Let the number = x
Doubled and 9 added = 2x + 9
Trebled: 3(2x + 9) = 75
2x + 9 = 25
2x = 16
x = 8
Hence, the number is 8.
Shortcut Method
Work backwards: 75 ÷ 3 = 25
= 25 − 9 = 16
= 16 ÷ 2 = 8
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. 65 litres water-contaminated milk was in a barrel where ratio between milk and water was 10 : 3. In that solution how much litre of water is to be mixed to get the ratio between milk and water as 8 : 5?
(A) 16 1/4 litres
(B) 1/4 litres
(C) 16 litres
(D) 17 litres
Answer & Explanation
Correct Answer: (A) 16 1/4 litres
Explanation
Total mixture = 65 L, Milk : Water = 10 : 3
Milk = 65 × 10/13 = 50 L
Water = 65 × 3/13 = 15 L
Let x litres of water be added
Milk : Water = 50 : (15 + x) = 8 : 5
8(15 + x) = 50 × 5
120 + 8x = 250
8x = 130
x = 16 1/4 litres
Hence, 16 1/4 litres of water must be added.
Shortcut Method
Milk stays 50 L = 8 parts
= 1 part = 6.25 L
= New water = 5 × 6.25 = 31.25 L
= 31.25 − 15 = 16.25 L
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The sum of two digits number and the number obtained by reversing the order of its digit is 121 and the difference of the digits is 3. The number is:-
(A) 85
(B) 63
(C) 74
(D) 96
Answer & Explanation
Correct Answer: (C) 74
Explanation
Let the number = 10a + b
Reversed number = 10b + a
Sum = (10a + b) + (10b + a) = 11(a + b)
11(a + b) = 121
a + b = 11
Difference of digits a − b = 3
2a = 14, so a = 7
b = 11 − 7 = 4
Number = 74 (the reversed number 47 also satisfies, and 74 is the option given)
Hence, the number is 74.
Shortcut Method
Option check: 74 → 7 + 4 = 11 and 7 − 4 = 3
= 74 + 47 = 121
Others fail: 85 → 8 + 5 = 13, 63 → 6 + 3 = 9, 96 → 9 + 6 = 15
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Simplify 9 ÷ [8 1/5 − {1 3/4 ÷ 3/4 + (6 − 3 3/5 + 1 2/3)}]
(A) 7
(B) 6
(C) 5
(D) 8
Answer & Explanation
Correct Answer: (C) 5
Explanation
Bracket ( ): 6 − 3 3/5 + 1 2/3 = 6 − 18/5 + 5/3
= (90 − 54 + 25)/15
= 61/15
Division: 1 3/4 ÷ 3/4 = 7/4 × 4/3
= 7/3
Curly bracket { }: 7/3 + 61/15 = (35 + 61)/15
= 96/15
= 32/5
Square bracket [ ]: 8 1/5 − 32/5 = 41/5 − 32/5
= 9/5
Final: 9 ÷ 9/5 = 9 × 5/9
= 5
Hence, the value of the expression is 5.
Shortcut Method
Use decimals: 1.75 ÷ 0.75 = 2.3333
= 6 − 3.6 + 1.6667 = 4.0667
= 2.3333 + 4.0667 = 6.4
= 8.2 − 6.4 = 1.8, and 9 ÷ 1.8 = 5
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. What will be the LCM of 8, 24, 36 and 54?
(A) 216
(B) 108
(C) 54
(D) 432
Answer & Explanation
Correct Answer: (A) 216
Explanation
Prime factors:
8 = 2³
24 = 2³ × 3
36 = 2² × 3²
54 = 2 × 3³
LCM = highest power of each prime
= 2³ × 3³
= 8 × 27
= 216
Hence, the LCM is 216.
Shortcut Method
Option check: 216 ÷ 8 = 27, 216 ÷ 24 = 9, 216 ÷ 36 = 6, 216 ÷ 54 = 4
= all exact
= 108 ÷ 8 = 13.5, so 108 fails
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. A grocer has a sale of Rs. 6,435, Rs. 6,927, Rs. 6,855, Rs. 7,230 and Rs. 6,562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6,500?
(A) Rs. 6,001
(B) Rs. 5,991
(C) Rs. 4,991
(D) Rs. 6,991
Answer & Explanation
Correct Answer: (C) Rs. 4,991
Explanation
Total of first 5 months = 6435 + 6927 + 6855 + 7230 + 6562
6435 + 6927 = 13362
13362 + 6855 = 20217
20217 + 7230 = 27447
27447 + 6562 = 34009
Total needed for 6 months = 6 × 6500 = 39000
Sixth month sale = 39000 − 34009
= Rs. 4,991
Hence, the grocer must sell goods worth Rs. 4,991 in the sixth month.
Shortcut Method
Deviations from 6500: −65, +427, +355, +730, +62
= total = +1509
= 6500 − 1509 = Rs. 4,991
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. Rs. 700 is divided among Ram, Shyam and Jadu so that Ram receives half as much as Shyam and Shyam half as much as Jadu. What will be Jadu’s share?
(A) Rs. 400
(B) Rs. 300
(C) Rs. 200
(D) Rs. 500
Answer & Explanation
Correct Answer: (A) Rs. 400
Explanation
Ram = (1/2) × Shyam and Shyam = (1/2) × Jadu
Let Jadu’s share = J
Shyam’s share = J/2
Ram’s share = J/4
J + J/2 + J/4 = 700
7J/4 = 700
J = 700 × 4/7
= Rs. 400
Hence, Jadu’s share is Rs. 400.
Shortcut Method
Ram : Shyam : Jadu = 1 : 2 : 4 (7 parts)
= 1 part = 700 ÷ 7 = Rs. 100
= Jadu = 4 × 100 = Rs. 400
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Q. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:-
(A) 46%
(B) 42%
(C) 40%
(D) 44%
Answer & Explanation
Correct Answer: (D) 44%
Explanation
Let original sides = l and b, area = lb
New length = 1.2l, new breadth = 1.2b
New area = 1.2l × 1.2b
= 1.44 lb
Increase = 1.44 lb − lb = 0.44 lb
Percentage increase = (0.44 lb/lb) × 100
= 44%
Hence, the area increases by 44%.
Shortcut Method
Increase % = x + y + (xy/100)
= 20 + 20 + (20 × 20)/100
= 40 + 4
= 44%
Want this as a PDF? Get the WBP SI Prelims PYQ PDF
Leave a Comment