At what time between 9 and 10 o'clock will the hands of a watch be together?

Answer: Option C

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
45 min. spaces are gained in
$$\left(\frac{60}{55}\times 45\right)\text{min}\text{.}\text{or}49\frac{1}{11}\text{min}.$$
∴ The hands are together at $$49\frac{1}{11}$$ min. past 9