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.