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...........

Quantitative Aptitude (CDS) Degree and Radian

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?

55.25 minutes

55.30 minutes

55-34 minutes

55-38 minutes

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Explanation:

Since hands are interchanging their position, minute hand is taking the place of an hour hand and an hour hand is taking the place of minute hand. So sum of the angles formed by h hand and minute hand = 360°

Let us assume that he was out of house for ‘t’ minutes.

So, the angle formed by minutes hand = 6 × t and by hour hand = 0.5 × t

So, 0.5 × t + 6 × t = 360

So, t = 55.38 minutes