At what time between 5 and 6 will the two hands of a watch coincide?

Explanation

The angle between the hour hand and the minute hand, $$ \theta = [30 H - 11 \frac{M}{2}] $$ H = 5 and $\theta = 0^\circ$ (When both the hands of the clock are together then $\theta = 0^\circ$) ∴ $\theta = [30 \times 5 - \frac{11 \times M}{2}]$ M = $\frac{150 \times 2}{11} = \frac{300}{11}$ M = $27\frac{3}{11}$ Therefore between 5 and 6 O’clock, both the clock hands will be coincide at 5O’clock 27.31 minutes. ## Page 50