A watch loses 2 minutes in every 24 hours while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is followed?
- (a) The two watches show the identical time again on completion of 30 days.
- (b) The two watches show the identical time again on completion of 90 days.
- (c) The two watches show the identical time again on completion of 120 days.
- (d) None of the above statements is correct. ✓ UPSC's answer
Why the answer is (d)
• One watch loses 2 minutes a day and the other gains 2 minutes a day, so the gap between them grows by 4 minutes a day.
• On a 24-hour clock they show the same time again only when the gap reaches 24 hours = 1,440 minutes.
• That takes 1,440 ÷ 4 = 360 days.
• After 30, 90 or 120 days the gap is only 120, 360 or 480 minutes, so none of (a)–(c) is correct: option (d).
Why the other options are wrong
- (a) The two watches show the identical time again on completion of 30 days.
- The watches will not show the identical time after 30 days because the relative difference would only be 120 minutes, which is not a multiple of 1440 minutes.
- (b) The two watches show the identical time again on completion of 90 days.
- The watches will not show the identical time after 90 days because the relative difference would only be 360 minutes, which is not a multiple of 1440 minutes.
- (c) The two watches show the identical time again on completion of 120 days.
- The watches will not show the identical time after 120 days because the relative difference would only be 480 minutes, which is not a multiple of 1440 minutes.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.