How many times do the two hands of a clock coincide in a day?

To determine how many times the two hands of a clock coincide in a day, we need to understand the movement of the clock hands and their relative speeds.

1. The hour hand completes a full revolution in 12 hours.
2. The minute hand completes a full revolution in 60 minutes.

Since there are 24 hours in a day, the hour hand will make two complete revolutions in a day. However, the minute hand will make 24 revolutions in a day.

To find the number of times the two hands coincide, we need to find the number of times the minute hand catches up with the hour hand.

3. The minute hand catches up with the hour hand once every hour. This happens when the minute hand is at the 12 o'clock position and the hour hand is at any other position.

Therefore, the two hands coincide 22 times in a day (since the minute hand catches up with the hour hand 11 times in the first 12 hours and 11 times in the next 12 hours).

In conclusion, the two hands of a clock coincide 22 times in a day.