Question

How many times in a day do a clock’s hands overlap?

Answer 1

22 times is the answer............

Answer 2

Let initially it over lapped at 12 o'clock
next overlap is after 1 o'clock
let it overlap after time t min
angle by both hand will be same, taking 12 o'clock as reference
after 1 o'clock hour hand will subtend an angle = 30° + 0.5t
and by minute hand, angle = 6t
A/q
 30° + 0.5t = 6t
⇒5.5t = 30
⇒t = 60/11
counting from 12 o'clock total time will be 65 min 5/11 sec
so for one overlap time interval is  65 min 5/11 sec
total min in one day = 24×60
total number of overlap = (24×60)/(720/11)
                                     =(24×60×11)/720 = 22
so total number of overlap will be 22