At what time between 7 and 8, are the hands of a clock coincides?

The correct answer is Option (1) → \(38\displaystyle\frac{2}{11}\) min past 7

The minute hand gains 55 minute-spaces in 60 minutes on the hour hand. At 7 o’clock the hour hand is 35 minute-spaces ahead, so the minute hand must gain 35 spaces to reach it.

• Time to gain 35 spaces \(=35\times\displaystyle\frac{60}{55}=\frac{420}{11}\) min

• \(\displaystyle\frac{420}{11}=38\frac{2}{11}\) min

So the hands coincide at \(38\frac{2}{11}\) minutes past 7.