Question

Between $1$ o'clock and $2$ o'clock, find the time when the minute hand and an hour hand are coinciding.

Answer 1

At $1$ o'clock, the minute hand is $5$ minutes behind the hour hand. The minute hand gains $5$ minutes in $5\times \frac{12}{11}$ minutes i.e, in $5\frac{5}{11}$ minutes. Thus the hands will coincide at $5\frac{5}{11}$ minutes past $1$ o'clock.