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How much does the clock gain or lose per...

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

A

(A). Loses `56""8/77` minutes

B

(B). Gains `56""8/77` minutes

C

(C). Loses `56""56/77` minutes

D

(D). Gains `75""75/341` minutes

Text Solution

Verified by Experts

The correct Answer is:
B
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 less than `65""5/11` minutes, then the clock gains time.
So, Gain in 63 minutes
`=(65""5/11-63)=(65+5/11-63)=(2+5/11)`
`=27/11" minutes "[therefore 65""5/11" can be written as "65+5/11]`
So, Gain in a day i.e. 24 hours
`" "=24 times 60 times 27/11 times 1/63=4320/77=56""8/7` minutes.
Therefore, the clock gains in a day i.e. in 24 hours
`" "=56""8/77` minutes.
Note : Use the formula : `" "`[ In case of gain]
If `x lt 65""5/11` then
Total time gained in T hours `=(T times 60){65""5/11-x}//x` minutes.
where x is the time in which the hands of the incorrect clock coincide.
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