How many times do the two hands of a clock coincide in a day?          a.24   b.22   c.48   d.12

To determine

To determine how many times the two hands of a clock coincide in a day, we need to consider the movement of the hour and minute hands.

1. The hour hand completes a full revolution in 12 hours, while the minute hand completes a full revolution in 60 minutes.
2. In one hour, the minute hand moves 12 times faster than the hour hand (since there are 60 minutes in an hour and 12 hours on the clock).
3. Therefore, the minute hand gains 11 positions on the hour hand in one hour.
4. To find the number of times the two hands coincide in a day, we need to calculate how many times the minute hand gains a full revolution on the hour hand.
5. In 12 hours, the minute hand gains 12 revolutions on the hour hand (since it gains 11 positions per hour).
6. In 24 hours (a full day), the minute hand will gain 24 revolutions on the hour hand.
7. Therefore, the two hands of a clock coincide 24 times in a day.

So, the correct answer is option a. 24.