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
5 minutes fast
Option(4) is correct.
Let the speed of man is x km/hr and the distance between his home and village is Y km.
Total time taken = 16:00 pm - 14:30 pm = \(3 \over 2\) hr
The total time during traveling ( excluding rest) = \(3 \over 2\) hr - \(25 \over 60\) hr = \(13 \over 12\) hr
Speed, distance, time equation :
\({Y \over X} + { 1.25Y \over 2X} = {13 \over 12} \) ⇒ \({Y \over X} = {2 \over 3} hr\) = 40 minutes
Hence, time is taken from home to village by man = 40 minutes
⇒ So exact time on Clock when man reached village = 14:30 pm + 40 minutes = 15:10 pm
The village clock shows 15:15 pm.
So, the Village clock is 5 minutes faster.
Hence, the correct answer is an option(4) i.e., 5 minutes fast.
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