Hello,

Please refer to the below formula whenever there is an overtaking of a minute hand and loss/gain of time involved:

(720/11-M)(24*60/M) min

where M= intervals of n minutes of correct time

Now, the minute hand of a clock overtakes the hour hand at intervals of 66 minutes of the correct time, therefore putting the value of m = 66 in the above equation, we get time gain or lose as:

(720/11-66)(24*60/66)

= - 1440/121 mins

Therefore, the clock will lose 1440/121 mins in 24 hours (Answer)