Question

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

(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 correct. 

Answer 1

Correct option (d) None of the above statements correct.

Explanation:

A watch loses 2 minutes in every 24 hours,while another watch gains 2 minutes in every 24 hours.Hence, every day the time difference between the two watches will keep on increasing by 4 minutes. They will again show the same identical time when this difference increases to 24 hours, i.e. 24 × 60 minutes. 

Now, for the difference to increase by 4 minutes it takes 1 day 

For the difference to increase by 24 × 60 minutes it will take (1/4) × 24 × 60 days = 6 × 60 days = 360 days