A person goes to a market between 4 pm and 5 pm when he comes back he finds that the hour hand and t...........

Quantitative Aptitude (CDS) Degree and Radian

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

55.38 min

55.48 min

55.57 min

55.67 min

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Explanation:

Since, both of the hands are interchanging there positions, minute hand is taking the place of the hour hand and the hour hand is taking the place of minute hand.
$\therefore$ Sum of the angles formed by hour and minute hand = 360°
Let us assume that he was out of house for t min.
So, the angle formed by minute hand = 6t
and the angled formed by hour hand = 0.5 t
So, 0.5t + 6t = 360
=> 6.5t = 360 => t = 360/6.5 = 55.38 min
Hence, the person was out of the house for 55.38 min.