QUESTION

CSAT

Easy

Maths

Prelims 2022

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

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Explanation

Total Time Taken for the Entire Journey: The man started at 14:30 hours and returned home by 16:00 hours, so the total time spent from departure to return is: 16:00 - 14:30 = 90 minutes.
Time Spent in the Village: The man stayed in the village for 25 minutes. Subtracting this time from the total journey time: 90 minutes - 25 minutes = 65 minutes (total travel time).
Using Time-Speed-Distance Formula: Let the distance to the village be $d$ , and the speed on the first leg of the journey be $s$ . From the return journey, we know the route is 1.25 times longer, and the speed is twice as fast. Therefore, the return trip time is: $\frac{1.25d}{2s}$ .

The total travel time is the sum of the time taken to reach the village and the time taken to return: $\frac{d}{s} + \frac{1.25d}{2s} = 65$ minutes.

Simplifying this equation: $\frac{d}{s} + \frac{1.25d}{2s} = 65$ . $\frac{2d}{2s} + \frac{1.25d}{2s} = 65$ $\frac{3.25d}{2s} = 65$ $\frac{d}{s} = \frac{65 \times 2}{3.25} = 40$ minutes.

Time Taken to Reach the Village: The time taken to reach the village was 40 minutes. Starting from 14:30, the man would have reached the village at: 14:30 + 40 minutes = 15:10 hours.
Village Clock Error: According to the village clock, he arrived at 15:15 hours. Therefore, the village clock is 5 minutes fast: 15:15 - 15:10 = 5 minutes fast.

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