Question

How many times are the hands of a clock at right angle in a day?

• A. 22
• B. 33
• C. 44
• D. 21

Answer 1

The Correct Option is C

The minute hand covers \(360\degree\) in an hour and \(6\degree\) in a minute.

The hour hand covers 30° in an hour and \(0.5\degree\) in a minute.

Calculation:

Starting from midnight i.e. 12 o clock at the midnight, the first time the difference between the two hands would be \(90\degree\) is:

\(6x=0.5x+90\degree\) (x is the number of minutes)

\(5.5x=90\degree\)

\(x=\frac{180}{11}\) minutes
The next time the difference between the two hands would be \(90\degree\) is when the minute hand would have moved \(180\degree\) away from the hour hand or the difference between both hands would have been \(270\degree\).

\(6x=0.5x+270\)

\(5.5x=270\)

\(x=\frac{540}{11}\) minutes

Thus, the difference between two consecutive moments where both hands forms a right angle is:

\(\frac{540}{11}-\frac{180}{11}=\frac{360}{11}\) minutes

Thus, the two hands form a right angle after every \(\frac{360}{11}\) minutes.

Total number of minutes in a day \(=24\times60=1440\) minutes.
Number of times the two hands will form a right angle in a day \(=\frac{1440}{(\frac{360}{11})}\)

\(\frac{(1440\times11)}{360}\)

\(4\times11=44\)
The correct option is (C):44