Question

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

• A. 24
• B. 48
• C. 22
• D. 44

Hint:

The hands of a clock form right angles twice every hour, except for the moments when they overlap.

Answer 1

The Correct Option is D

In a 12-hour period, the hands of a clock form a right angle 22 times.
Therefore, in a full 24-hour day, the hands of the clock will form a right angle 44 times.

Thus, the correct answer is 44.

Answer 2

We need to find how many times the hands of a clock are at right angles in a full day (24 hours).

Right Angle Between Clock Hands:
The hands of a clock are at right angles when the angle between them is exactly 90° or 270°.
This happens twice every hour:
- Once when the minute hand is 90° ahead of the hour hand.
- Once when it is 90° behind the hour hand.

Number of Right Angles in 12 Hours:
Since there are 2 right angles every hour,
in 12 hours, the number of right angles = 2 × 12 = 24.

Number of Right Angles in 24 Hours:
In a full day (24 hours), the hands will be at right angles twice the 12-hour count:
24 × 2 = 48 times.

Correction for Overlaps:
However, the hands are exactly at right angles 44 times in 24 hours,
because of the fact that some right angles coincide exactly with overlaps or straight lines,
and the exact number is 44, not 48.

Summary:
- Hands of a clock are at right angles twice every hour.
- Normally 48 times in 24 hours.
- Actual count considering exact positions is 44 times.