# Q. A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1.25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

a. 10 minutes slow

b. 5 minutes slow

c. 10 minutes fast

d. 5 minutes fast

Correct Answer: d. 5 minutes fast

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

Let’s break down the given information and solve the problem step by step:

## The man started from home at 14:30 hours and arrived at the village when the village clock indicated 15:15 hours.

He stayed in the village for 25 minutes.

He drove back home by a different route, which was 1.25 times the first route, and at a rate twice as fast as the first route.

He reached home at 16:00 hours.

First, we need to calculate the time taken for each part of the trip:

Total time taken by the man to come back home: 16:00 – 14:30 = 1.5 hours = 90 minutes

Out of which he stayed in the village for 25 minutes.

So, his total traveling time = 90 – 25 = 65 minutes

Let’s denote the time taken for the first route as 100 units. Since the return route was 1.25 times the initial route, the time taken would have increased by 25%. So, the time taken for the second route would be 125 units.

But it is also given that while returning he drove twice as fast, which means the time taken must have been halved. So, the time taken while returning is 62.5 units.

Therefore, the total traveling time can be represented as:

100 units (first route) + 62.5 units (second route) = 65 minutes

162.5 units = 65 minutes

Now, we can find out the actual time taken for the first route:

100 units = (65/162.5) × 100 = 40 minutes

So, the man took 40 minutes to reach the village. The actual time at that moment was:

14:30 (start time) + 40 minutes (travel time) = 15:10 hours

Comparing the village clock with the actual time:

15:15 (village clock) – 15:10 (actual time) = 5 minutes

Hence, the village clock is 5 minutes fast. The correct answer is: d. 5 minutes fast