The minute-hand of a clock overtakes the hour-hand at intervals of 65 minutes of the correct time. How much in a day does the clock gain or lose?
None of these
In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour
55 min. are gained in 60 min.
60 min is gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =(720/11)-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =1440/143
The clock gains 1440/143 minutes in 24 hours.
Option 3 is the answer.