A man started from home at 14:30 hours and drove to a 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

Re-check: Let onward time be t minutes. Return distance = 1.25 times onward distance, speed = 2 times, so return time = (1.25/2)t = 0.625t. Total elapsed home-clock time from 14:30 to 16:00 = 90 min, including 25 min stay: t + 25 + 0.625t = 90 ⇒ 1.625t = 65 ⇒ t = 40 min.

So he reached the village at 15:10 by home clock. The village clock showed 15:15, hence the village clock was 5 minutes fast.

• (a) 10 minutes slow: Actual difference is not 10 minutes, and the clock is not slow. Incorrect.
• (b) 5 minutes slow: Magnitude 5 is right, but direction is wrong. Incorrect.
• (c) 10 minutes fast: Clock is fast, but only by 5 minutes. Incorrect.
• (d) 5 minutes fast: Village clock reads 5 minutes ahead of home clock. Correct.