arithmetic - the minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time how much a day does the clock gain or lose - skillgun

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 hand. 55 min. are gained in 60 min.
60 min are gained in (60 x 60)/55 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min=720/11-65 =5/11 min.
Gain in 24 hours =(5/11 * (60*24)/65)min =440/43
The clock gains 440/43 minutes in 24 hours.