At what time between 5 and 6 o’clock do the hands of a clock coincide?

The correct answer is Option (1) → \(27 \frac{3}{11}\) min past 5

The minute hand moves 60 minute spaces in an hour and the hour hand 5, so the minute hand gains 55 minute spaces every 60 minutes. The hands coincide when the minute hand has made up the gap between them at 5 o’clock.

• At 5:00 the hour hand is on the 5, that is, \(5\times5=25\) minute spaces ahead of the minute hand

• Time to gain 25 spaces \(\displaystyle =25\times\frac{60}{55}=\frac{300}{11}=27\frac{3}{11}\) min

Tip: Between \(h\) and \(h+1\) o’clock the hands coincide at \(\displaystyle \frac{60h}{11}\) min past \(h\), since the minute hand must make up \(5h\) spaces at \(\frac{11}{12}\) of a space a minute.