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) Time and work

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 the minute hand of the clock have interchanged their positions. For how much time (approximately) was he out of his house?

55.38 minutes

55.48 minutes

55.57 minutes

55.67 minutes

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Explanation:

Since two hands are interchange their positions so sum of the angles subtended at the centre by hour hand and minute hand = 360°.

Let us suppose that she was out of house for t min. So the sum of angles subtended at the centre by the hour hand and minute hand.
Angle made by hour hand.
i.e., 12h -> 360°
⇒ 1h =360/12= 30°
⇒ 1min =30/60= 0.5 min
Angle made by minute hand.
60 min = 360°
1 min = 60
(0.5) t + (6 × t) ° = 360°= 55.38 min.