Other than noon and midnight ,how many times do the hour and minute hands cross each other

Question

My question is about aptitude and maths included

 

Answer 1

1 day = 24 hours.

 

The minute hand covers 360 degrees in 60 minutes.  That's 6 degrees per minute.

 

The hour hand covers 360 degrees in 12 hours (that is, 720 minutes).  That's 1/2 degree per minute.

 

The angular relative speed between the minute hand and the hour hand is  6–1/2 = 11/2 degrees per minute.

 

Starting at 12:00, the hands overlap when the relative distance between them covers 360 degrees.  T = D/R

             360/(11/2) = 720/11 minutes = 65.45 minutes = 1 hour 5 minutes 27 seconds

 

How many times is that in 12 hours?

       (number of minutes)/(720/11)

               12*60/(720/11)

                   11 times

 

Other than noon and midnight, there are 10 times.  They are:

   1:05:27   2:10:54   3:16:21   4:21:48   5:27:15   6:32:42   7:38:09   8:43:37   9:49:04   10:54:32   

Answer 2

Every one hour and 5 minutes...

 

12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, 10:50.