How much does the clock gain or lose per day if its hands coincide every 63 minutes ?

Options

A. Gains in `80""80/341` minutes
B. Gains in `92""244/253` minutes
C. Loses in `80""80/253` minutes
D. Loses in `73""251/253` minutes

Answer

D

Explanation

As we know that in a correct clock, the hands of a clock coincide every `65""5/11` minutes. But in case of incorrect clocks, if the hands of a clock coincide is greater than `65""5/11` minutes, then the clock loses time.
So, Loss in 69 minutes
`" "=(69-69""5/11)={69-(65+5/11)}`
`" "=(4-5/11)=39/11` minutes
So, Loss in day i.e., 24 hours
`" "=24 times 60 times 39/11 times 1/69`
`" "18720/253=73""251/253` minutes
Therefore, the clock loses in a day i.e. in 24 hours
`" "=73""251/253` minutes. Note : Use the formula : `" "` [In case of loss]
If `x gt 65""5/11`, then Total time lost in T hours
`" "=(T times 60){x-65""5/11)//x` minutes.
where x is the time in which the hands of the incorrect clock coincide.