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

Answer: Option D

At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in
$$\begin{array}{rl}& \left(\frac{60}{55}\times 50\right)\text{min}\text{.}\text{or}54\frac{6}{11}\text{min}.\\ & \therefore \text{Required}\text{time}\\ & =54\frac{6}{11}\text{min}\text{.}\text{past}4\end{array}$$