In 12 hrs. the hands of the clock will be perpendicular to each other for 22 times as in 1 hr. time the hands of the clock wil be at rt. angles for 2 times but between 1 1'o clock and 1'o clock they will be at rt. angles only twice.
Therefore, in 24 hrs. they will be at right angles 44 times.
Edit: Thank you Robin for providing an alternative solution in the comments.
Easy Time And Work Question - 8
How many times will minute hand and hour hand opposite in one day?
Eleven times in 12 hrs. The hands will be directly opposite each other at the following times:
12:32 and 8/11 of a minute
1:38 and 2/11 of a minute
2:43 and 7/11 of a minute
3:49 and 1/11 of a minute
4:54 and 6/11 of a minute
7:05 and 5/11 of a minute
8:10 and 10/11 of a minute
9:16 and 4/11 of a minute
10:21 and 9/11 of a minute
11:27 and 3/11 of a minute.
Therefore, the hands of the clock will be opposite to each other 22 times.