UPSC CDS Math Speed, Time and Distance Questions

Let the person be out of his house for t minutes.
It is given that the hour hand and minute hand had interchanged their positions.
Therefore, angle formed by the minute hand in t minutes + Angle formed by the hour hand in t minutes = 360°
⇒6×t+

1

2

t=360
⇒t=

360

6.5

=55.38 minutes (approx.)