How many times are the hour and the minute hands of a clock at a right angle in a period of two days?

Concept: The minute hand covers 360° in an hour and 6° in a minute.
The hour hand covers 30° in an hour and 0.5° in a minute.
Solution:
Starting from midnight i.e. 12 o'clock at midnight, the first time the difference between the two hands would be 90° is:
6x = 0.5x + 90° (x is the number of minutes)
=> 5.5x = 90°
=> x = 180/11 minutes
The next time the difference between the two hands would be 90° is when the minute hand would have moved 180° away from the hour hand or the difference between both hands would have been 270°.
6x = 0.5x + 270
=> 5.5x = 270
=> x = 540/11 minutes
Thus, the difference between two consecutive moments where both hands form a right angle is:
540/11 - 180/11 = 360/11 minutes
Thus, the two hands form a right angle after every 360/11 minutes.
​Total number of minutes in a day = 24 × 60 = 1440 minutes.
Number of times the two hands will form a right angle in a day = 1440 ÷ (360/11)
=> (1440 × 11) ÷ 360
=> 4 × 11 = 44 times
So, hour and the minute hands of a clock at a right angle in a period of two days: