How Many Times a Day Minute and Hour Hand Overlap?
How many times a day do the minute and hour hand overlap? If you are a job seeker then this is a common question you have to face in your job interview. This is a hot question of job viva board.
Though the board members do not expect the exact answer. They want to see how the interviewee cope up and handle situation like this.
How Many Times Do The Hands On A Clock Overlap?
At the first time you might think the answer will be 24 times. But you are wrong, the correct answer is 22 times a day.
When do the hands on a clock overlap?
The hands of your watch will meet 22 times in a day. This is because the hands overlap at 12:00, 1:05, 2:11, 3:16, 4:22. 5:27, 6:33, 7:38, 8:44, 9:49, 10:54. The 11 times that the hands overlap happen twice in a day, so the total number of times the hands meet is 22.
From the following figure we easily understand that the hands do not overlap only 11th hour. So technically, the answer to this question is that the hands never meet at the 11th hour.
Though you think this is one kind of funny question, but the answer is not funny. This can be solved by algebraic manipulation.
The hour hand move 1/12 of a lap while the minute hand complete a cycle around the dial.
The hands overlap once when during completing a cycle by the minute hand but they hour hand shift by a small portion. As a result, after 11th hour they overlap a 12 o’clock. So during 12 hours they meet 11 times instead of 12.
So from the above thoughts give an equation that x= x/12 + N.
Where, x=total number of hours;
N= number of times hands overlap.
x = x/12 + N
-N = x/12 -x
-N = 24/12 – 24
-N = 12 – 24
-N = -22
N = 22
After todays whenever you face this question in job viva or tea party, then you find yourself different than others. Since you not only know the answer, you also know the math with this.
These pictures show the eleven times minute and hour hands overlap:
