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Question

A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and minute hand have interchanged their positions. For how much time (approximately) was he out of his house?

A
55.25 minutes
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B
55.30 minutes
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C
55.34 minutes
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D
55.38 minutes
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E
None of these
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Solution

The correct option is D 55.38 minutes
Let us assume that he was out of the house for 't' min.
So angle formed by min hand =6×t
Angle formed by hour hand = 0.5×t
Now, 0.5 × t + 6 × t = 360
6.5 t=360
6.5 t=360t=3606.5=55.38 min

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