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

2
by khushi786
I think the answer is 22 times.
me too

2016-01-24T12:56:37+05:30
22 times is the answer............
• qais
• Content Quality
2016-01-27T17:53:27+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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