NIMCET 2020 — Reasoning PYQ

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Question

NIMCET 2020 — Reasoning PYQ

NIMCET | Reasoning | 2020

Mr. Kumar drives to work at an average speed of 48 Km/hr. The time taken to cover the first 60% of the distance is 10minutes more than the time taken to cover the remaining distance. How far is his office?

Choose the correct answer:

Explanation

Let the total distance to the office be $d$ km.

1. Break down the distances:

First part of the distance ( $60%$ of $d$ ): $0.6 d$
Remaining part of the distance ( $100% - 60% = 40%$ of $d$ ): $0.4 d$

2. Relate distance to time:

The formula for time is:

$Time = \frac{Distance}{Speed}$

Given that the average speed for the entire journey is 48 Km/hr:

Time taken for the first part: $t_{1} = \frac{0.6 d}{48}$
Time taken for the remaining part: $t_{2} = \frac{0.4 d}{48}$

3. Set up the equation:

The difference between the two times is 10 minutes. Since the speed is in Km/hr, we must convert 10 minutes into hours:

$10 minutes = \frac{10}{60} hours = \frac{1}{6} hour$

According to the question:

$t_{1} - t_{2} = \frac{1}{6}$

$\frac{0.6 d}{48} - \frac{0.4 d}{48} = \frac{1}{6}$

4. Solve for $d$ :

Combine the fractions on the left side:

$\frac{0.6 d - 0.4 d}{48} = \frac{1}{6}$

$\frac{0.2 d}{48} = \frac{1}{6}$

Multiply both sides by 48:

$0.2 d = \frac{48}{6}$

$0.2 d = 8$

$d = \frac{8}{0.2}$

$d = 40 Kms$

Correct Answer: B) 40 Kms