At what time between 5:30 and 6 will the hands of a clock be at right angles?

Answer: Option B

At 5 o'clock, the hands are 25 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
$$\begin{array}{rl}& =\left(\frac{60}{55}\times 40\right)\min .\\ & =43\frac{7}{11}\min .\\ & \therefore \text{Required time}=43\frac{7}{11}\min .\text{past}5\end{array}$$