The minutes hand of a clock overtakes the hours hand every 64 minutes of the correct time, how many mintes does the clock lose or gain in a day of normal time?

Solution(By Examveda Team)

First calculate the interval of time it should take the minute hand to overtake the hour hand.

Let
x = distance traveled by hour hand
1 + x = distance traveled by minute hand

Time = Distance/Rate
x/(1/12) = (1 + x)/1
x = (1/12)(1 + x) = 1/12 + x/12
(11/12)x = 1/12
x = 1/11

Calculate time for minute hand to travel a distance 1 + x.

Time = Distance/Rate
(1 + x)/1 = 1 + x = 1 + 1/11 = 12/11 hour

Actual time to overtake on clock is 64 minutes.

64 min = 64/60 hours = 16/15 hour

Correct Clock Speed/Actual Clock Speed
(12/11) / (16/15) = 12*15 / (11*16) = 180/176 = 45/44

The clock gains:
45/44 - 1 = 1/44 day = 24/44 hour = 6/11 hour = 360/11 min