Question

Two clocks are set to show the correct time at 1:00am on a day. One clock loses 3 minutes in an hour and the other clock gains 3 minutes in an hour. Exactly after how many days will both the watches show the correct time? Assume that is a 12 hour clock.

• A. 30 days
• B. 10 days
• C. 15 days
• D. 5 days

Answer 1

The correct option is A

30 days

Every clock shall display the correct time when it is late or fast by hours which are a multiple of 12 .

As per the question, the first clock loses 3 minutes in an hour. Therefore, to lose 12 hours, it will take $\frac{12\times 60}{3}=240$ hours =10 days.

Also, the second clock gains 2 minutes inan hour. Therefore, to gain 12 hours, it will take : $\frac{12\times 60}{2}=360$ hours = 15 days.

Therefore, after 30 days (LCM of 15 and 10), both the watches will show the correct time .