Quantitative Aptitude - MCQ Practice Questions

A's rate = $\frac{1}{12}$, B's rate = $\frac{1}{18}$.

Combined rate = $\frac{1}{12}$ + $\frac{1}{18}$ = $\frac{3}{36}$ + $\frac{2}{36}$ = $\frac{5}{36}$.

Time = $\frac{36}{5}$ = 7.2 days

Combined rate = $\frac{1}{10}$ + $\frac{1}{15}$ + $\frac{1}{30}$ = $\frac{3}{30}$ + $\frac{2}{30}$ + $\frac{1}{30}$ = $\frac{6}{30}$ = $\frac{1}{5}$.

Time = 5 days

A completes $\frac{1}{3}$ work in 5 days, so rate = $\frac{1}{15}$ per day.

Remaining work = $\frac{2}{3}$.

Days needed = ($\frac{2}{3}$)/($\frac{1}{15}$) = ($\frac{2}{3}$) × 15 = 10 days

Combined rate = $\frac{1}{8}$, A's rate = $\frac{1}{12}$. B's rate = $\frac{1}{8}$ - $\frac{1}{12}$ = $\frac{3}{24}$ - $\frac{2}{24}$ = $\frac{1}{24}$. B takes 24 days

A's rate = $\frac{1}{12}$, B's rate = $\frac{1}{18}$. Combined rate = $\frac{5}{36}$. In 6 hours, they fill $\frac{30}{36}$ = $\frac{5}{6}$. Remaining = $\frac{1}{6}$. Time for A alone = ($\frac{1}{6}$)/($\frac{1}{12}$) = 2 hours. Total = 6+2 = 8 hours. But with both for 6 hrs: ($\frac{5}{36}$)×6 = $\frac{5}{6}$ filled. Remaining $\frac{1}{6}$ by A: 2 hours. Check: Total effective = 4 hours additional work needed.

Item 1: CP=500, SP=600 (20% gain). Item 2: CP=500, SP=425 (15% loss). Total CP=1000, Total SP=1025. Profit=25. Percentage = 2.5%

P's rate = $\frac{1}{30}$, Q's rate = $\frac{1}{40}$. Combined = $\frac{7}{120}$. In 10 days: 10 × $\frac{7}{120}$ = $\frac{7}{12}$ completed. Remaining = $\frac{5}{12}$. Q's time = ($\frac{5}{12}$)/($\frac{1}{40}$) = $\frac{5}{12}$ × 40 = 16.67 ≈ 15 days

Combined rate = $\frac{1}{6}$ + $\frac{1}{8}$ + $\frac{1}{10}$ = $\frac{20}{120}$ + $\frac{15}{120}$ + $\frac{12}{120}$ = $\frac{47}{120}$. Time = $\frac{120}{47}$ ≈ 2.73 hours

Let CP = 100. MP = 140. SP = 140 × $\frac{80}{100}$ = 112. Profit = 12%

When two trains move towards each other, their relative speed is the sum of their individual speeds, and they must cover a combined distance equal to the sum of their lengths.

Step 1: Convert speeds to m/s

Speed is given in km/h; convert to m/s by multiplying by $\frac{5}{18}$:

Step 2: Find relative speed (trains moving towards each other)

When trains move towards each other, relative speed is the sum:

Or more precisely: \(v_{\text{relative}} = \frac{25}{2} + \frac{50}{3} = \frac{75 + 100}{6} = \frac{175}{6} \text{ m/s}\]

Step 3: Find total distance to be covered

For the trains to completely cross each other, the combined distance equals the sum of their lengths:

Step 4: Calculate time to cross

Using $t=\frac{d}{v}$:

**Answer: The trains will take $12$ seconds to cross each other. (Option B)**

Let B = 100, A = 120. Difference = 20. Percentage less = ($\frac{20}{120}$) × 100 = 16.67%

A's rate = $\frac{1}{18}$, B's rate = $\frac{1}{12}$. B alone for 3 days = $\frac{3}{12}$ = $\frac{1}{4}$. Remaining = $\frac{3}{4}$. Combined rate = $\frac{1}{18}$ + $\frac{1}{12}$ = $\frac{5}{36}$. Time together = ($\frac{3}{4}$)/($\frac{5}{36}$) = $\frac{27}{5}$ = 5.4 ≈ 5 days

Let CP = 100. MP = 150. SP = 150 × $\frac{80}{100}$ = 120. Profit = 20. Profit% = 20%.

[Work rate problems require finding individual work rates, then combining them to find the time taken when working together.]

Step 1: Find A's Work Rate

A completes $\frac{1}{3}$ of work in 5 days, so we calculate how much work A does per day.

Step 2: Find B's Work Rate

B completes $\frac{2}{3}$ of work in 10 days, so we calculate how much work B does per day.

Step 3: Find Combined Work Rate

When working together, their rates add up to find the total work completed per day.

Step 4: Find Time to Complete Entire Work

To complete 1 full work at a combined rate of $\frac{2}{15}$ per day, divide total work by combined rate.

A can do

3

1

​

of the work in 5 days.

So, A’s one-day work:

5

$\frac{1}{3}$

​

=

15

1

​

B can do

3

2

​

of the work in 10 days.

So, B’s one-day work:

10

$\frac{2}{3}$

​

=

30

2

​

=

15

1

​

Together, one-day work:

15

1

​

+

15

1

​

=

15

2

​

Time taken to complete the whole work:

$\frac{2}{15}$

1

​

=

2

15

​

=7.5

Therefore, together they can complete the work in:

7.5 days

​

Answer: B) 7.5 days

Savings = 100 - 25 - 30 = 45%. If 45% = 9000, then 100% = 9000 × $\frac{100}{45}$ = 20,000.

A's rate : B's rate = 3:2. Let A's rate = 3x, B's rate = 2x. Combined = 5x = $\frac{1}{10}$. So x = $\frac{1}{50}$. A's rate = $\frac{3}{50}$, time = $\frac{50}{3}$ ≈ 16.67 days.

To find the difference between compound interest and simple interest, we calculate both separately using the given principal, rate, and time period.

Step 1: Calculate Simple Interest

Simple interest is calculated using the formula $SI=\frac{P\times R\times T}{100}$, where $P$ is principal, $R$ is rate, and $T$ is time.

Step 2: Calculate Compound Interest

Compound interest is found using $A=P{\left(1+\frac{R}{100}\right)}^T$, then $CI=A-P$.

Step 3: Find the Difference

The difference between compound interest and simple interest is:

Answer: The difference is ₹32 (Option A)

Work is proportional to number of men. If work increases by 50%, men needed = M × 1.5 = 1.5M.

Let A's cost = x. B's cost = 1.2x. C's cost = 1.2x × 1.25 = 1.5x = 7500. x = 5000.

Rate = $\frac{1}{12}$ + $\frac{1}{15}$ - $\frac{1}{20}$ = (5+4-3)/60 = $\frac{6}{60}$ = $\frac{1}{10}$. Time = 10 hours.