The correct answer is Option (3) → 44 times
The Calculation
- In 1 hour: Generally, the hands are at a right angle 2 times every hour.
- In 12 hours: If the hands were at a right angle twice every hour, you would expect 24 times ($12 \times 2$). However, there is a "loss" of frequency during specific periods.
- The Exceptions: Between 2 and 4 o'clock and 8 and 10 o'clock, the hands are at a right angle only 3 times (instead of 4) for each 2-hour interval. This happens because the right angle exactly at 3:00 and 9:00 is "shared" or counted within those blocks.
- Right angles in 12 hours: $24 - 2 = 22 \text{ times}$.
- In 24 hours: Since there are 22 occurrences in 12 hours, in a full day (24 hours), the hands are at a right angle $22 \times 2 = \mathbf{44 \text{ times}}$.
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