Solution:
24 times is the most common answer however that is completely wrong. The right answer will be 22 times.
Let us prove it by some simple mathematics.
Assume that it takes T hours for the minute hand to complete T laps. The hour hand will complete T/12 Laps in the same time.
Consider the situation when the hour hand and the minute hand will overlap for the first time; the minute hand would have completed one lap extra than the hour hands.
Thus, T =T/12 + 1
Considering the above expression we know that the first overlap will take place after t = 12/11 hours i.e. 1:05 am.
Similarly, the second overlap will take place when the minute hand would have completed two more laps than the hour hand.
Considering there are X laps,
T = T/12 + X
Everyone knows that a day comprises of 24 hours. Putting that in the equation we get
24 = 24/12 + X
Solve it and you will get
X = 22
Hence both of the hands will overlap 22 times in 24 hours.
Let us give you with those exact timings as well.
The hands will overlap at 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, and 10:50. Do consider the fact that there will be no 11:55. It becomes 12:00.