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

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

Solution:
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 = (60/55) × 45
= (60 × 9)/11
= 540/11

∴ The hands are together at 540/11 min. past 9