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?

Correct Option (4)

The first watch loses 2 minutes every 24 hours, and the second watch gains 2 minutes every 24 hours. Consequently, the relative difference in time between the two watches accumulates at a rate of 2 minutes (gain) + 2 minutes (loss) = 4 minutes per day.

For the two watches to display the identical time again, the cumulative time difference between them must equal a full 24-hour cycle. A 24-hour cycle comprises 24 × 60 = 1440 minutes.

The number of days required for this 1440-minute difference to accumulate is calculated as: 1440 minutes / 4 minutes/day = 360 days.

Since the calculated period for the watches to show identical time again is 360 days, and this value is not presented in options 1, 2, or 3, option 4 is the correct choice.

Incorrect Options:

Options 1, 2, and 3 are incorrect because the watches will show identical time again after 360 days, not after 30, 90, or 120 days. The calculation demonstrates that a cumulative difference of 1440 minutes (one full 24-hour cycle) is achieved after 360 days, given a daily relative difference of 4 minutes.