Question

One day I found a strange thing happening to my watch,the minute hand & the hour hand were coming together every 65 minutes.I decided to get it checked. Was my watch gaining or losing time, and how much per hour?

Answer 1

Explanation:

The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.

Here M = 64. The clock gains or losses in a day by

=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)

=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.