At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

Answer: Option D

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in
$$\begin{array}{rl}& =\left(\frac{60}{55}\times 5\right)\min .\\ & =5\frac{5}{11}\min .\\ & \therefore \text{Required time}=5\frac{5}{11}\min .\text{past}7\end{array}$$