Answer: (C) She suffers a loss of 1%.

Explanation

When two items are sold at the same selling price and the gain and loss percentages are equal, the overall result is always a loss. The loss percentage is given by:$$\text{Loss \%}=\frac{(\text{Gain/Loss \%})^2}{100}=\frac{10^2}{100}=1\%$$

Hence, Punam suffers a loss of 1%.

Answer: (B) 2

Explanation

This is a derangement problem, where no letter is placed in its correct envelope. The number of derangements of 3 objects is:$$!3 = 2$$!3=2

The two possible arrangements are:

• (2, 3, 1)
• (3, 1, 2)

Hence, the number of ways is 2.

Answer: (C) 80%

xplanation

Use the alligation method:$$\text{Boys : Girls} = (50 – 42) : (52 – 50) = 8 : 2 = 4 : 1$$

Thus, boys constitute 4 out of 5 students.$$\text{Percentage of boys} = \frac{4}{5} \times 100 = 80\%$$

Hence, the percentage of boys in the class is 80%.

Answer: (A) 2 : 1

Explanation

Let the number of cows be $x$x and crows be $y$y.

Since there are 30 heads:$$x + y = 30$$

Since cows have 4 legs and crows have 2 legs:
$$4x + 2y = 100$$

Substituting $y = 30 – x$:$$4x + 2(30 – x) = 100$$ 2x=40⇒x=20,y=10

Thus, the ratio of cows to crows is $20:10 = \mathbf{2:1}$.

Answer: (A) 16 m/s

Explanation

When equal distances are covered at different speeds, the average speed is the harmonic mean:$$\text{Average Speed}=\frac{2v_1v_2}{v_1+v_2}$$

Substituting $v_1=10$ m/s and $v_2=40$ m/s:
$$\frac{2\times10\times40}{10+40}=\frac{800}{50}=16\text{ m/s}$$

Hence, the average speed of the body is 16 m/s.

Answer: (C) 115

Explanation

Let the number of correct, unattempted, and wrong answers be $C$C, $U$U, and $W$W, respectively.

Then,$$C+U+W=30,\qquad \text{Score}=4C+U$$

Checking the options:

• 113: $C=28,\ U=1,\ W=1$ ✓
• 114: $C=28,\ U=2,\ W=0$ ✓
• 115: Requires $4C+U=115$, but no non-negative integers $C,U,W$ satisfy both conditions. ✗
• 117: $C=29,\ U=1,\ W=0$ ✓

Hence, 115 is not attainable.

Answer: (C) 30

Explanation

Since all installments are equal, the fraction of the loan repaid equals the fraction of installments paid.

Let the total number of installments be $x$.
$$\frac{18}{x}=\frac{60}{100}=\frac{3}{5}$$$$x=\frac{18\times5}{3}=30$$

Hence, the total number of installments was 30.

Answer: (B) decrease by 4%.

Explanation

Let the original length and breadth be $L$ and $B$. The new dimensions are:
$$0.8L \quad \text{and} \quad 1.2B$$

Hence, the new area is:$$0.8L \times 1.2B = 0.96LB$$

Thus, the new area is 96% of the original area, i.e., it decreases by 4%.

Answer: (B) $x = 6,\; y = 8$

Explanation

From $\frac{x}{y} = \frac{3}{4}$​, let $x = 3k$ and $y = 4k$.

Substituting into $2x – 3y = -12$:
$$2(3k) – 3(4k) = -12$$$$6k – 12k = -12 \Rightarrow -6k = -12 \Rightarrow k = 2$$

Hence,$$x = 3 \times 2 = 6,\qquad y = 4 \times 2 = 8.$$

Therefore, the correct answer is (B) x=6,  y=8x = 6,\; y = 8x=6,y=8.

Answer: (A) 10:10 am

Explanation

Since the cars move towards each other, their relative speed is:$$50 + 30 = 80 \text{ km/h}$$

Time taken to meet:$$\frac{160}{80} = 2 \text{ hours}$$

Starting at 8:10 am, they meet after 2 hours, i.e., at 10:10 am.

Answer: (B) 500 m

Explanation

When a train passes through a tunnel, it covers a distance equal to:
$$\text{Length of train} + \text{Length of tunnel}$$

Distance covered in 2 minutes:$$60 \times \frac{2}{60} = 2 \text{ km}$$

Therefore,$$\text{Length of train} = 2 – 1.5 = 0.5 \text{ km} = 500 \text{ m}$$

Hence, the length of the train is 500 m.

Answer: (A) A quadrilateral cannot be a square unless it has four equal sides, but having four equal sides doesn’t guarantee a quadrilateral to be a square.

Explanation

A necessary condition is one that must be satisfied for a statement to be true. Every square has four equal sides, so this condition is necessary.

However, it is not sufficient because a quadrilateral with four equal sides can also be a rhombus, which need not have four right angles. Therefore, having four equal sides alone does not guarantee that the quadrilateral is a square.

Answer: (D) 6

Explanation

Let the first row contain $a$ children. Then the rows form an arithmetic progression with common difference $-3$.

For 6 rows:$$\frac{6}{2}\,[2a+(6-1)(-3)] = 630$$$$3(2a-15)=630$$$$6a=675 \Rightarrow a=112.5$$

Since the number of children cannot be fractional, 6 rows are not possible. Hence, the correct answer is (D) 6.

Answer: (A) 4%

Explanation

Using the principle of inclusion-exclusion:
$$\text{Failed in at least one subject} = 55 + 65 – 24 = 96\%$$

Therefore,$$\text{Passed in both subjects} = 100\% – 96\% = 4\%$$

Hence, 4% of the candidates passed in both subjects.

Answer: (C) 7

Explanation

Classes VI to VIII have 3 classes, each with 6 periods:
$$3 \times 6 = 18 \text{ periods}$$

Classes IX and X have 2 classes, each with 7 periods:
$$2 \times 7 = 14 \text{ periods}$$

Total periods per day:$$18 + 14 = 32$$

Since one teacher can take at most 5 periods per day,
$$\frac{32}{5} = 6.4$$

So, the minimum number of teachers required is 7.

Answer: (B) 12

Explanation

Let the number of ₹200 notes be $x$ and ₹100 notes be $y$.

Then,$$x+y=48$$ $$200x+100y=6000$$

Dividing the second equation by 100:$$2x+y=60$$

Subtracting the first equation:$$(2x+y)-(x+y)=60-48$$ $$x=12$$

Hence, the number of ₹200 notes is 12.

Answer: (B) 0.02

Explanation

Rewrite each factor as:$$1-\frac{1}{n}=\frac{n-1}{n}$$

So,$$\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\cdots\times\frac{99}{100}$$

This is a telescoping product, where all intermediate terms cancel out, leaving:
$$\frac{2}{100}=\frac{1}{50}=0.02$$

Hence, the correct answer is 0.02.

Answer: (D) 40

Explanation

Let the number of correct answers be $x$. Then the number of incorrect answers is $75-x$.

The total score is:$$2x-(75-x)=45$$ $$3x-75=45$$ $$3x=120 \Rightarrow x=40$$

Hence, the student answered 40 questions correctly.

Answer: (A) 10

Explanation

Using the formula for permutations:
$${}^nP_4=n(n-1)(n-2)(n-3)=5040$$

Checking the options:

For $n=10$,$$10 \times 9 \times 8 \times 7 = 5040$$

Hence, the required value of $n$ is 10.

Answer: (C) 12½ cm

Explanation

Convert the ratio into whole numbers by taking the LCM of $20, 15,$ and $12$, which is $60$:
$$\frac{1}{20} : \frac{1}{15} : \frac{1}{12} = 3 : 4 : 5$$

The sum of the ratio is $3+4+5=12$. Since the perimeter is $30$ cm, one part is:
$$\frac{30}{12}=2.5\text{ cm}$$

The biggest side is:$$5 \times 2.5 = 12.5\text{ cm}$$

Hence, the length of the biggest side is 12½ cm.

Answer: (B) 55

Explanation

The total runs scored by the five batsmen are:
$$5 \times 35 = 175$$

Let $E=x$. Then:

• $D=x+5$
• $A=x+20$
• $B=D+E=2x+5$

Since $B+C=75$,$$A+B+C+D+E=(A+D+E)+75=175$$$$(x+20)+(x+5)+x+75=175$$$$3x+100=175 \Rightarrow x=25$$

So,$$B=2(25)+5=55$$

Hence,$$C=75-55=20$$

Therefore, the correct answer is (C) 20.

Answer: (A) f(x)

Explanation

Substitute $-x$ for $x$:$$f(-x)=5^{-x}+\frac{1}{5^{-x}}+2$$

Since $5^{-x}=\frac{1}{5^x}$ and $\frac{1}{5^{-x}}=5^x$,$$f(-x)=\frac{1}{5^x}+5^x+2 =5^x+\frac{1}{5^x}+2 =f(x)$$

Hence, f(−x)=f(x), so the correct answer is (A).

Answer: (D) 12

Explanation

Initially, each boy has 10 cards.

• E borrows 2 cards? Actually, E borrows 3 cards from A → $D$ remains 10.
• E gives 5 cards to C → $D$ remains 10.
• C gives 4 cards to B → $D$ remains 10.
• B gives 2 cards to D → $D = 10 + 2 = 12$.

Hence, D has 12 cards at the end.

Answer: (D) 9

Explanation

Use the identity:$$(a+b)(a-b)=a^2-b^2$$

Here,$$8798 \times 8792=(8795+3)(8795-3)=8795^2-3^2=8795^2-9$$

Therefore, adding 9 gives:$$8795^2-9+9=8795^2,$$

which is a perfect square. Hence, the least number to be added is 9.

Answer: (B) 15

Explanation

Each match is played between a pair of players. Therefore, the total number of matches is the number of ways to choose 2 players from 6:
$${}^6C_2=\frac{6\times5}{2}=15$$

Hence, the total number of matches played in the tournament is 15.

Answer: (C) 82.5

Explanation

Length of cloth to be excluded:$$40 – 7 = 33 \text{ metres}$$

Percentage excluded:$$\frac{33}{40}\times 100 = 82.5\%$$

Hence, 82.5% of the cloth should be excluded.

Answer: (D) 69

Explanation

For 6 consecutive odd numbers, the average is the average of the 3rd and 4th numbers.

Let the numbers be:$$59,\ 61,\ 63,\ 65,\ 67,\ 69$$

Their average is:$$\frac{63+65}{2}=64$$

Hence, the greatest of the six consecutive odd numbers is 69.

Answer: (A) 7

Explanation

Let the number of cows be $C$C and hens be $H$H.

Then,

• Total heads $= C+H$
• Total legs $= 4C+2H$

According to the question:$$4C+2H = 2(C+H)+14$$ $$4C+2H = 2C+2H+14$$ $$2C=14 \Rightarrow C=7$$

Hence, the number of cows is 7.

Answer: (A) 50 years

Explanation

Let the present ages of the father, elder son, and younger son be $F$, $E$, and $Y$ respectively.

Given:$$F = 2E,\qquad E – Y = 15$$

Also, after 10 years:$$F + 10 = 3(Y + 10)$$

Substituting $F = 2E$ and $Y = E – 15$:
$$2E + 10 = 3(E – 15 + 10)$$$$2E + 10 = 3E – 15$$ $$E = 25$$

Hence,$$F = 2 \times 25 = 50$$

However, this value is not among the options if we follow the given equations carefully. Rechecking:$$Y = 25 – 15 = 10,\quad F = 50$$

After 10 years:

• Father = $60$
• Younger son = $20$

Since $60 = 3 \times 20$, all conditions are satisfied.

Therefore, the correct age of the father is 50 years, and the correct answer is (A) 50 years.

Answer: (C) $\frac{4}{5}$

Explanation

Convert the fractions into decimals:$$\frac{3}{4}=0.75,\qquad \frac{5}{6}\approx0.833$$

Checking the options:

• $\frac{2}{3}\approx0.667$ ✗
• $\frac{1}{2}=0.5$ ✗
• $\frac{4}{5}=0.8$ ✓
• $\frac{9}{10}=0.9$ ✗

Hence, the fraction lying between $\frac{3}{4}$​ and $\frac{5}{6}$​ is $\frac{4}{5}$

.

Answer: (C) 200 days

Explanation

Total food available $= 4000 \times 190 = 760000$

Food consumed in the first 30 days:
$$4000 \times 30 = 120000 \text{ man-days}$$

Remaining food:$$760000 – 120000 = 640000 \text{ man-days}$$

After 800 men leave, the remaining men are:
$$4000 – 800 = 3200$$

Hence, the remaining food will last:
$$\frac{640000}{3200} = 200 \text{ days}$$

Therefore, the correct answer is (C) 200 days.

Answer: (B) ₹2,400

Explanation

The selling price (SP) is ₹2,280, which is 95% of the cost price (CP) because the loss is 5%.$$\text{CP}=\frac{2280 \times 100}{95}=2400$$

Hence, the fruit seller spent ₹2,400 in purchasing the basket of mangoes.

Answer: (A) 1 : 12

Explanation

The minute hand completes one revolution in 60 minutes (1 hour), while the hour hand completes one revolution in 12 hours.

Therefore, their angular speeds (velocities) are in the ratio:
$$\frac{1}{12} : 1 = 1 : 12$$

Hence, the velocity ratio of the hour hand to the minute hand is 1 : 12.

Answer: (A) 100.101

Explanation

Convert the integer and fractional parts separately:

• $4_{10} = 100_2$​
• $0.625 = \frac{1}{2} + \frac{1}{8} = 0.101_2$

Therefore,$$4.625_{10} = 100.101_2$$

Hence, the correct answer is (A) 100.101.

Answer: (C) 120 feet

Explanation

Under similar conditions, the ratio of height to shadow remains constant.
$$\frac{64}{96}=\frac{H}{180}$$$$H=\frac{64\times180}{96}=120\text{ feet}$$

Hence, the height of the telephone tower is 120 feet.

Answer: (A) 18 seconds

Explanation

Since the train and the man are moving in the same direction, the relative speed is:
$$41 – 11 = 30 \text{ km/h} = 30 \times \frac{5}{18}=\frac{25}{3}\text{ m/s}$$

Time taken to pass the man:
$$\frac{\text{Length of train}}{\text{Relative speed}} =\frac{150}{25/3} =\frac{150\times3}{25} =18\text{ seconds}$$

Hence, the train will pass the man in 18 seconds.

Answer: (B) 68%

Explanation

Number of students not enrolled in NCC:
$$1500 – 480 = 1020$$

Percentage of students not in NCC:
$$\frac{1020}{1500}\times100 = 68\%$$

Hence, 68% of the students are not enrolled in NCC.

Answer: (B) 3¾ hrs

Explanation

Mohan’s work rate is $\frac{1}{6}$​ job/hour and Laltu’s work rate is $\frac{1}{10}$ job/hour.

Combined work rate:$$\frac{1}{6}+\frac{1}{10}=\frac{5+3}{30}=\frac{8}{30}=\frac{4}{15}$$

Time taken together:$$\frac{1}{4/15}=\frac{15}{4}=3.75\text{ hours}=3\frac{3}{4}\text{ hours}$$

Thus, the correct answer is 3¾ hours.

Answer:(C) $\sqrt{75816}$​cm

Explanation

The wall, ground, and ladder form a right-angled triangle. Using the Pythagoras theorem:$$\text{Length of ladder}=\sqrt{270^2+54^2}$$$$=\sqrt{72900+2916} =\sqrt{75816}\ \text{cm}$$

Hence, the length of the ladder is $\sqrt{75816}$​cm.

Answer: (D) Rs. 400

Explanation

Manoj’s typing rate:$$\frac{100}{10}=10 \text{ pages/hour}$$

Bobby’s typing rate:$$\frac{100}{15}=\frac{20}{3} \text{ pages/hour}$$

Together, in 5 hours they complete:
$$5\left(10+\frac{20}{3}\right) =5\times\frac{50}{3} =\frac{250}{3}=83\frac{1}{3}\text{ pages}$$

Remaining work:$$100-83\frac{1}{3}=16\frac{2}{3}=\frac{50}{3}\text{ pages}$$

Lucy completed $\frac{50}{3}$ pages, i.e., $\frac{1}{6}$ of the total work.

Therefore, Lucy’s share of ₹2400 is:$$\frac{1}{6}\times2400=₹400$$

Hence, the correct answer is (D) Rs. 400.

Answer: (A) 1 : 8

Explanation

Convert both quantities to the same unit.
$$4\text{ feet} = 4 \times 12 = 48\text{ inches}$$

Therefore,$$6 : 48 = 1 : 8$$

Hence, the required ratio is 1 : 8.

Answer: (B) The 71st day

Explanation

The caterpillar gains a net 1 inch per day (5 inches up and 4 inches down). On the 70th night, it is at 70 inches.

On the 71st day, it climbs 5 inches from 70 inches to 75 inches, reaching the top before it can slide down at night.

Hence, the caterpillar first reaches the top on the 71st day.

Answer: (B) 99

Explanation

Given,$$x_i+x_{i+1}=100$$

and $x_{10}=1$.

So,$$x_9=99,\quad x_8=1,\quad x_7=99,\quad x_6=1,\ \ldots$$

The values alternate between 99 and 1. Since $x_{10}$ is an even-indexed term and equals 1, all even-indexed terms are 1 and all odd-indexed terms are 99.

Therefore,$$\boxed{x_1=99}$$

Hence, the correct answer is (B) 99.

Answer: (A) $x=2,\;y=-1,\;z=3$

Explanation

First,$$216^{\frac{2}{3}}=(6^3)^{\frac{2}{3}}=6^2=36.$$

Also,$$\left(\frac{p^2}{9}\right)^{-\frac{3}{2}} =\left(\frac{9}{p^2}\right)^{\frac{3}{2}} =\frac{27}{p^3}.$$

Therefore,$$36\div\frac{27}{p^3} =36\times\frac{p^3}{27} =\frac{4}{3}p^3 =2^2\cdot3^{-1}\cdot p^3.$$

Hence,$$\boxed{x=2,\;y=-1,\;z=3}$$

So, the correct answer is (A).

Answer: (B) 21

Explanation

In a knock-out tournament, each match eliminates one participant.

Starting with 22 participants, 21 participants must be eliminated to leave one winner.

Therefore, the total number of matches required is:
$$22 – 1 = 21$$

Hence, the correct answer is (B) 21.

Answer: (A) 64800 m/day.

Explanation

There are:$$24 \times 60 \times 60 = 86400 \text{ seconds in a day}$$

Distance travelled in one day:$$75 \times 86400 = 6480000 \text{ cm}$$

Since,$$6480000\text{ cm} = 64800\text{ m}$$

the correct value is 6480000 cm/day or 64800 m/day.

Note: The question contains a printing error. Both Option (A) = 64800 m/day and Option (C) = 6480000 cm/day represent the same distance. Hence, the mathematically correct distance is 64800 m/day = 6480000 cm/day.

Answer: (A) 720°

Explanation

The sum of the interior angles of an $n$-sided polygon is given by:
$$(n-2)\times180^\circ$$

For a hexagon ($n=6$):$$(6-2)\times180^\circ=4\times180^\circ=720^\circ$$

Hence, the sum of all the interior angles of a hexagon is 720°.