# Aptitude - Clock - Discussion

Discussion Forum : Clock - General Questions (Q.No. 17)
17.
How many times do the hands of a clock coincide in a day?
20
21
22
24
Explanation:

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

AM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

PM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

Discussion:
11 comments Page 1 of 2.

AbineshKarna said:   4 years ago
How it is possible? I am not understanding. Please tell me.

Please explain in an easy way. Why does the hands of a clock coincide every 65min? Please tell me.

Anil kumar reddy said:   6 years ago
You just missed 11:10 AM, the hands coincide for 23 times a day.

Priya said:   7 years ago
I can't understand the explanation. Give in easy way.

Neha said:   7 years ago
HH and MH coincide between A and B when x = 60*(A/11), i.e they will meet at 'x' minutes past A.

In every hour, both the hands coincide, when they both start moving from the same position, after (360*2/11) = 65 5/11 minutes.

What is the difference between these two points I mentioned above?

Vishal Mittal said:   8 years ago
Ok I got it.

There is no need to learn this thing that much tough.

Just remember clock overlaps after 65 min thus.

A day has 24*60 = 1440 min.

Then, no of overlap, say n = 1440/65 = 22.22.

Which is absolute 22. Thus answer is 22.

Theja said:   8 years ago
The explanation given says 10:55 but at 10:50 the hands coincide and the count of 11:55 isn't taken which happens twice?

Anurag Nayak said:   9 years ago
Hi Raju,

1) Start at 12.

2) After 60 min that is 1 pm. difference is still 5 min.

3) Now minute hand has to travel some extra minute to make the angle between them zero.

theta = 30h -11/2m.
theta = 0.
m = 60/11.

So 60 + 60/11 = 60*12/11.

So after every 60*12/11 min..the clock will coincide ..
In a day there is 1440 min.

1440/(60*12/11) = 22.

Jpdsgil said:   9 years ago
Dear Raju,

Each 5min. space is equivalent to 360°/12=30°

The hour hand rotates (360/12)°/60min. = 0.5°/min.
The minute hand rotates 360°/60min. = 6°/min.

Suppose that the clock says 01:00 and let H be the angle between the noon and the hour hand. If we want to know at what time the hands will coincide:

H+0.5*t = 6*t.

However, if it is 01:00, we also know that H=30°, thus:

30+0.5*t = 6*t => t=5.454545....

Therefore, (60+5.4545)min. are needed so that both hands coincide AND NOT 60min.

If you do the same for H=60° (02:00), you'll have:

60+0.5*t = 6*t => t=10.9090.

It means we have to wait (120 + 10.9090)min. SINCE THE BEGINNING before the hands coincide a second time.

The difference between the time at which the hands coincide a second time and the time at which the hands coincide for the first time is:

(120+10.9090)-(60+5.4545) = 60+5.454545.

Obviously, this is the time we need to wait for the hands to coincide a third time.

Raju said:   9 years ago
Who said it overlaps after every 65min?