Question

How many times in a day do the two hands on a clock coincide?

Answer 1

Hint: Here we will first find after how much time both hands coincides. Using this we will find the number of times the two hands coincides in a 12 hour span. Then we will multiply the result obtained by 2 to get the number of times the two hands coincide in a day.

Complete step-by-step answer:
We know that the minute and hour hand coincide every 65 minutes and not 60 minutes.
Also, the hour and minute hand coincide only once between 11 and 1 o’clock i.e. at 12 o’clock.
So, from both the above statements we can say that the two hands coincide exactly 11 times in a 12 hour span.
We have to find the number of times in a day so we have 24 hours in a day. Therefore,
The number of times the two hands coincide \[ = 2 \times 11 = 22\] times.

So, the number of times the two hands coincide in a day is 22 times.

Note:
We can solve this question using another method also. We know that both hands coincide every 65 minutes we get the approx. value of the number of times the hands coincide.
As there are 24 hours in a day and we know that there is 60 minutes in an hour.
So, we get total minute in a day \[ = 24 \times 60 = 1440\min \]
As, both hands coincide after every 65 minutes so we will divide the above value by 65 and get,
The number of times the two hands coincide \[ = \dfrac{{1440}}{{65}}\]
Dividing the terms, we get
\[ \Rightarrow \] The number of times the two hands coincide \[ = 22.15 \approx 22\] times.