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)

['- The first watch loses 2 minutes per day, and the second watch gains 2 minutes per day, resulting in a relative rate of change of 4 minutes per day between the two watches.', '- For the watches to show the identical time again on a 24-hour clock, the accumulated relative difference must be an exact multiple of 24 hours (1440 minutes).', '- The time required for the relative difference to reach 1440 minutes is calculated as 1440 minutes / 4 minutes per day = 360 days.', '- Since 360 days is not equal to 30, 90, or 120 days, none of the specific timeframes mentioned in options (a), (b), or (c) are correct.', '- Therefore, the correct statement is that none of the above statements is correct.']

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.