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At watch, which gains uniformly, is 3 mi...

At watch, which gains uniformly, is 3 minutes slow at 12 noon on Sunday and is 5 minutes 36 seconds fast at 4 pm on the next Sunday. At what time it was correct ?

A

(A). 12 am on same day

B

(B). 12 pm on Monday

C

(C). 12 am on Tuesday

D

(D). 12 am on Wednesday

Text Solution

Verified by Experts

The correct Answer is:
D
According to the question,
Total time from Sunday noon (12 pm) to 4 pm the next Sunday = 7 days 4 hours = 172 hours.
Also, the watch gains in 172 hours = 3 minutes + 5 minutes 36 seconds `=3+5""36/60=(3+5""3/5)` minutes
`" "=43/5` minutes.
So, the watch gains 3 minutes in `=(3/(43/5)) times 172" hours"`
`" "=((3 times 5 times 172)/43)" hours".`
`" "` = 60 hours = 2 days 12 hours.
Therefore, the watch is correct after 2 days 12 hours from Sunday 12 noon = 12 am on Wednesday.
[`because` 2 days 12 hours + 12 hours = 2 days 24 hours = 3 days]
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