Question

Between $1$ o'clock and $2$ o'clock, find the time when the minute hand and an hour hand are straight line, i.e, in opposite direction.

Answer 1

When the hands are in opposite direction, the difference is $30$ minutes. So the minute hand has to gain $(5+30)$ min. i.e. $35$ minutes which it can do in $35\frac{12}{11}$ minutes i.e. $38\frac{2}{11}$ minutes. The time is $38\frac{2}{11}$ minutes past $1$ o'clock.