How many times in a day are the hands of clock pointing opposite to each other?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 22
The hands point in opposite directions when the minute hand is 180° ahead of the hour hand. The minute hand gains 330° an hour on the hour hand, so it gains a full 360° on it in \(\displaystyle\frac{12}{11}\) hours; that is, the hands come opposite once every \(\displaystyle\frac{12}{11}\) hours.
In 12 hours: \(12\div\displaystyle\frac{12}{11}=11\) times
In a day (24 hours): \(2\times11=22\) times
The count is 11 and not 12 in every 12 hours because the two cases between 5 and 7 o’clock merge into one, at 6 o’clock.
Tip: In a day the hands coincide 22 times, are opposite 22 times and are at right angles 44 times; these counts are worth memorising.