I went out between 2 and 3 and returning home between 7 and 8 found that the clock hands had exactly changed places. Find the time of my departure.

Options

A. 2:30
B. 2:00
C. 2:45
D. 2:35

Explanation

It will be easily seen that the same relative position of the hands will be repeated as soon as the MH will gain 60 minute-divisions on the HH. Now the MH will gain 60 minute-divisions in `(60/55 =)12/11` hours. This means that the relative position will be repeated at intervals of `12/11` hours.
Since `12/11` hours are contained in 12 hours `(12-:12/11 =)` 11 times, hence any relative position of the hands is repeated 11 times in 12 hours.