At what time between 2 o'clock and 3 o'clock will the hour and minute hands of a watch be together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(10\frac{10}{11}\) min past 2
The minute hand turns \(6^\circ\) a minute and the hour hand \(0.5^\circ\) a minute, so the minute hand gains \(5.5^\circ\) a minute on the hour hand. At 2 o’clock the hour hand is at the 2, \(60^\circ\) ahead of the minute hand at the 12; the hands meet when the minute hand has made up this gap.
Gap at 2:00 \(=2\times30^\circ=60^\circ\)
Time to make it up \(\displaystyle =\frac{60}{5.5}=\frac{120}{11}=10\frac{10}{11}\) min
The hands are together at \(10\frac{10}{11}\) min past 2
Shortcut: Between H and (H + 1) o’clock, the hands are together at \(\frac{60H}{11}\) minutes past H.
For H \(=2\): \(\displaystyle \frac{120}{11}=10\frac{10}{11}\) min past 2