At what time between 6 and 7 o'clock will the hand of a watch coincide.

Options

A. `6:32(8/11)`
B. `6:34(8/11)`
C. `6:33(8/11)`
D. `6:32(6/11)`

Answer

A

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.