At what time between 5.30 and 6 will the hands of a clock be at right angles?

A. 40 min. past 5
B. 42 min. past 5
C. 43 4/11 min past 5
D. 43 7/11 min. past 5
Ans: D.

Explanation:

At 5 o’clock, the hands are 24 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in [60/55 * 40] min. = 43 7/11 min.
=> Required time = 43 7/11 min. past 5.