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

A. 54 6/11 min. past 4
B. 50 min. past 4
C. 45 min past 4
D. 40 min past 4
Ans: A.

Explanation:

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 [60/55 * 50] min. or 54 6/11 min.
=> Required time = 54 6/11 min. past 4.