UPSC 2015 CDS I Math Paper

Let the person be out of his house for t minutes.
Since the hands are interchanging their positions, the minute hand is taking the place of the hour hand and the hour hand is taking the place of the minute hand. So, the sum of the angles formed by hour hand and minute hand = 360°
We know that :
Angle moved by the minute hand in 1 minute = 6°
Angle moved by the hour hand in 1 minute =

1°

2

⇒6×t+

1

2

×t=360
⇒6.5t=360
⇒t=

360

6.5

=55.38minutes