Ramu purchased a second hand Swiss watch which is very costly. In this watch the minute-hand and hour hand coincide after every $\displaystyle 65 \frac {3} {11} $ minutes. How much time does the watch lose or gain per day?

In a correctly functioning clock, the minute and hour hands coincide every 720/11 minutes, which equals 65 5/11 minutes. The defective watch coincides every 65 3/11 minutes, meaning it covers the required interval 2/11 minutes faster than a standard clock. This 2/11 minute error occurs every 65 3/11 minutes, so multiplying by 24 hours and the standard 1440 minutes in a day gives a total gain of 4 minutes per day.

• Thanks
• Wrong explanation