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

Answer: (C)

44

Answer 2

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