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
- (a) 10 minutes slow
- (b) 5 minutes slow
- (c) 10 minutes fast
- (d) 5 minutes fast ✓ UPSC's answer
Why the answer is (d)
• Let the outward drive take t minutes (by the home clock). The return route is 1·25 times as long and driven at twice the speed, so it takes 1·25 ÷ 2 = 5/8 of t.
• From 14:30 to 16:00 is 90 minutes: t + 25 (stay) + 5t/8 = 90, so 13t/8 = 65 and t = 40 minutes.
• He therefore reached the village at 14:30 + 40 min = 15:10 by the home clock (check: return takes 25 minutes, 15:35 + 25 min = 16:00).
• The village clock showed 15:15 at that moment, so it is 5 minutes fast, option (d).
Why the other options are wrong
- (a) 10 minutes slow
- The village clock read 15:15 when the true (home) time was 15:10, so it is 5 minutes fast, not 10 minutes slow.
- (b) 5 minutes slow
- The village clock read 15:15 when the true (home) time was 15:10, so it is fast, not slow.
- (c) 10 minutes fast
- The outward drive took 40 minutes, so the gap is 5 minutes, not 10.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.