I was asked this question in an entrance exam.
In one day, how many times the hour hand and the minute hand of a clock are at right angles to each other?
My answer was 48. My reasoning was that during any duration of an hour, the minute hand would come at right angle with the hour hand and then it will spin to a direction opposite to its previous direction in a duration less than that of an hour and thus making another right angle with the hour hand. In this way, they got perpendicular twice an hour. Hence 24 hours a day should make them 48 times perpendicular in an entire day.
But many sources suggested an answer of 44. Could someone point out the flaw in my reasoning and justify the correct answer?