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

The man started from home at 14:30 and returned home at 16:00. Total time spent away from home, according to the home clock = 16:00 - 14:30 = 1 hour 30 minutes = 90 minutes. During this 90 minutes, he stayed in the village for 25 minutes. So, the total driving time (to and fro), according to the home clock = 90 minutes - 25 minutes = 65 minutes. Let L be the length of the first route and V be the speed to the village. Time taken to drive to the village (T1) = L/V. The return route length is 1.25 times the first route = 1.25L. The return speed is twice as fast = 2V. Time taken to drive back (T2) = (1.25L) / (2V) = (1.25/2) * (L/V) = 0.625 * (L/V) = 0.625 * T1. We know that total driving time T1 + T2 = 65 minutes. Substitute T2: T1 + 0.625*T1 = 65 minutes. 1.625 * T1 = 65 minutes. T1 = 65 / 1.625 = 40 minutes. So, according to the home clock, the man took 40 minutes to drive to the village. He started at 14:30. Therefore, he arrived at the village at 14:30 + 40 minutes = 15:10 (according to the home clock). However, the village clock indicated 15:15 hours when he arrived. Comparing the arrival time on the home clock (15:10) with the village clock (15:15), the village clock is 5 minutes ahead. Thus, the village clock is 5 minutes fast. The final answer is D) 5 minutes fast.