**In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times.**

Angular speed of hour hand is 0.5^{°}/minute.

Angular speed of minute hand is 6^{°}/ minute.

Relative to hour hand , the angular speed of minute hand is 5.5^{°} per minute.

The hour hand stops rotating , minute hand moves slower than before)

At 12 O clock, the angle is zero.

90/ 5.5 gives 16.3636363636 minutes

There are 1440 minutes in 24 hour .

1440/ 16.36 is 88 ( rounded)

This is for the 4 quadrants .

But we have to consider only 2 quadrants.

Therefore the answer is

** 88/ 2 = 44**