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

Correct Answer: (D) 5 minutes fast

Total time elapsed on the home clock between departure (14:30) and return (16:00) is 90 minutes. Subtracting the 25 minutes spent at the village leaves a total driving time of 65 minutes. Let the outward travel time be $t$. Since the return route has $1.25$ times the distance at $2$ times the speed, return travel time is $\frac{1.25}{2}t=\frac{5}{8}t$$\frac{1.25}{2}$t = $\frac{5}{8}$t. Thus, $t +$$\frac{5}{8}$t = 65 $\implies$ $\frac{13}{8}$t = 65 $\implies$ t = 40$\text{ minutes}$. Departure was at 14:30, so the actual arrival time at the village was $14:30 + 40$$\text{ min}$ = 15:10. Because the village clock read 15:15 upon arrival, it is 5 minutes fast.