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Question

At what time between 4and 5, will the hands of a clock coincide ?


A

15.81min

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B

21.81min

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C

23.81min

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D

33.48min

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Solution

The correct option is B

21.81min


The minute hand of a clock covers 3600 in 60min or 60 in 1min.

The hour hand of a clock covers 3600 in 12hrs or 300 in 1hour or 0.50 in 1min.

At 4:00, the minute hand has covered 00 and the hour hand has covered 1200.

Let the time after which the hands coincide be xmin.

So, the hour hand covers 120+x2up to that time and the minute hand covers 6x0 up to that time. When they coincide the angles should be the same.

So we can write 120+x2=6x

12x-x2=12011x=240x=24011min=21.81min

Hence, the correct option is B.


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