A clock shows 1 o’clock. When will its hour hand and minute hand next lie exactly one over the other?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5\(\frac{5}{11}\) minutes past 1
The minute hand gains \(6^\circ-0.5^\circ=5.5^\circ\) a minute on the hour hand. It catches up when it has made up the gap between the hands.
At 1:00 the hour hand is at 30° from 12 and the minute hand at 0°: gap \(=30^\circ\)
Minutes needed \(\displaystyle =\frac{30}{5.5}=\frac{60}{11}=5\frac{5}{11}\)
So the hands are next together at \(5\frac{5}{11}\) minutes past 1
At 5 minutes past 1 the minute hand is on the 1, but the hour hand has already moved \(5\times0.5^\circ=2.5^\circ\) beyond it, so the hands are not yet together
