Question

Andy notices that the hands on his watch overlap multiple times in a day. Help him find how many times in an entire day the hour hand meets the minute hand.

• A. 21 times
• B. 22 times
• C. 23 times
• D. 24 times

Answer 1

The correct option is B 22 times

The day starts at 12:00 am with both the hands at 12.


To meet with the hour hand again, the minute hand has to go around the watch's face atleast once.

Examining the watch's face an hour later, we find:


Examining the watch a further 5 minutes later, we find:

Hence, the hands overlap every 1 hour and 5 minutes or every 65 minutes.

$1day=24hours$

So,

$Numberofoverlapsin1day=24\times Numberofoverlapsin1hour$

But,

$Numberofoverlapsin1hour=\frac{Minutesinanhour}{Minuteselapsedfromoneoverlaptothenext}=\frac{60}{65}=\frac{60÷5}{65÷5}=\frac{12}{13}$

Hence,

$Numberofoverlapsin1day=24\times \frac{12}{13}$

$=\frac{288}{13}$

$=22.15$

As the number of overlaps cannot be a decimal, we take the nearest whole number that is lower than the decimal.

Therefore, in an entire day, the hour hand meets the minute hand 22 times.