At what time between 5 and 6 o'clock will the hour and minute hands of a clock coincide?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(27\frac{3}{11}\) min past 5
The minute hand moves 6° a minute and the hour hand 0.5° a minute, so the minute hand gains 5.5° every minute. At 5 o'clock it is behind the hour hand by \(5\times30=150^\circ\), and the hands coincide when it has made up that gap.
Gap at 5:00 \(=150^\circ\)
Time to gain 150° \(\displaystyle=\frac{150}{5.5}=\frac{300}{11}=27\frac{3}{11}\) minutes, so the hands coincide at \(27\frac{3}{11}\) minutes past 5