How many times the hands of a clock are at right angle in a day?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 44
The hands are at a right angle whenever the minute hand is 90° ahead of or behind the hour hand, so this happens twice each time the minute hand gains one full round on the hour hand.
In 12 hours the minute hand goes round 12 times and the hour hand once, so the minute hand gains 11 rounds
Two right angles in each round: \(11\times2=22\) times in 12 hours
A day has two such 12-hour periods: \(22\times2=44\) times
Tip: It is not 48 (twice an hour), because around 3 o’clock and 9 o’clock two right angles of neighbouring hours fall at the same moment; so 22 in 12 hours, 44 in a day.