Question

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.

Answer 1

(d) None of the above statements is correct.

A watch loses 2 minutes in every 24 hours, while another watch gains 2 minutes in every 24 hours.

Therefore, every day(24 hours) the time difference between the two watches will keep on increasing by 4 minutes. This means that the two watches will again show the same identical time when this difference increases to 24 hours, i.e.

24 × 60 minutes = 1440 minutes. 

By unitary method,

The difference of 4 minutes is reached in 1 day.

The difference of 1 minutes is reached in 1/4 day.

The difference of 1440 minutes is reached in 1440/4 = 360 days.

Hence, None of the above statements is correct.