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

Here's a step-by-step breakdown:

1. Calculate total time elapsed by home clock: The man started at 14:30 and returned at 16:00. Total time = 16:00 - 14:30 = 1 hour 30 minutes = 90 minutes.

2. Calculate total driving time: He stayed for 25 minutes in the village. So, the total time spent driving = Total time - Stay time = 90 minutes - 25 minutes = 65 minutes.

3. Relate outward and return journey times:

   • Let the distance to the village be D1 and speed be S1. Time for outward journey (T1) = D1/S1.
   • For the return journey, distance D2 = 1.25 * D1 and speed S2 = 2 * S1.
   • Time for return journey (T2) = D2/S2 = (1.25 * D1) / (2 * S1) = (1.25/2) * (D1/S1) = 0.625 * T1.

4. Calculate outward journey time (T1):

   • Total driving time = T1 + T2 = T1 + 0.625 * T1 = 1.625 * T1.
   • We know total driving time is 65 minutes. So, 1.625 * T1 = 65 minutes.
   • T1 = 65 / 1.625 = 65 / (13/8) = 65 * 8 / 13 = 5 * 8 = 40 minutes.

5. Determine actual arrival time at the village: The man started at 14:30 and drove for 40 minutes. So, he actually arrived at the village at 14:30 + 40 minutes = 15:10 (according to an accurate clock, like his home clock).

6. Compare with village clock: When he arrived, the village clock indicated 15:15. His actual arrival time was 15:10.

   • Village clock reading (15:15) - Actual time (15:10) = 5 minutes.
   • Since the village clock showed a later time, it is 5 minutes fast.

The final answer is D) 5 minutes fast.