Question

At what the time required between $4$ and $5$ o'clock will the hands of a watch point in opposite directions?

Answer 1

When we observe the clock,

At $4$ o’clock, the hands of the watch are $20min.$ spaces apart.
So to be in opposite directions, the time be $30min.$ spaces apart.
$\therefore$ The minute hand will have to gain $50min.$ space.
$55min.$ spaces are gained in $60min.$
$50min.$ spaces are gained $=\left(\frac{60}{55}\right)\times 50$

$=54\frac{6}{11}$

So, the required time $=54\frac{6}{11}min.past4$

Hence, the time required between $4$ and $5$ o'clock will the hands of a watch point in opposite directions is $54\frac{6}{11}min.past4$.