Question

How many times do the hands of clock points towards each other in a day?

Answer 1

let start from midnight 12 am or 0 hours.  The two hands point in the same direction.

The minutes  hand turns 360 degrees in one hour. So  in one hour  the minutes hand must meet the hours hand..

angle covered by hours hand = 360 / 12 = 30 deg / hour = 1/2 deg /minutes
angle covered by minutes hand = 360/ 60 min = 6 deg / min. 

Let us say that the two hands meet after a period of T minutes.

       1/2 * T = 6 * T - 360
           11 T /2 = 360        T = 720/11 = 65 min + 5/11 minutes

  in 24 hours,    24 * 60 / T =  24 * 60 * 11 / 720 = 22 times they meet