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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The hands of a clock coincide 22 times in a day. The hands of a clock move every minute and every hour. The minute hand moves faster than the house hand. Thus, if the hands make 12 rounds every 12 hours, they would coincide 12 times. However, the hands only coincide once between 11 and 1. Hence, the total time the hands of a clock coincide in 12 hours is 11 times. Hence, the in a day they coincide 22 times.

Table of content

1. Times Hands of a Clock Coincide in a Day
2. Steps To Calculate How Many Times Hands of a Clock Coincide in a Day
3. How many times do the hands of a clock coincide in a day?

Times Hands of a Clock Coincide in a Day

22 times the hands of a clock coincide in a day. One might think the hands of a clock coincide every 60 minutes, however, in reality, they coincide every 65 minutes. Considering this, they coincide 11 times every 12 hours. This means that the hands of a clock coincide 22 times in a day which consists of 24 hours.

Considering the movement of the minute hand and the hour hand, the exact times at which the clock coincides twice a day, i.e. in am and pm include the following: 12:00, 1:05, 2:11, 3:16, 4:22, 5:27, 6:32, 7:38, 8:44, 9:49, 10:55.

Steps To Calculate How Many Times Hands of a Clock Coincide in a Day

Another way to find out the number of times the hands of a clock coincide in a day is to calculate it mathematically. As we have established above, the hands of a clock coincide every 65 minutes. This is approximate, taking which we can calculate the number of times minute and hour hands will coincide.

There are 24 hours in a day. Each hour has 60 minutes. Thus, in a day there are a total of 1440 minutes

Considering the hands of a clock coincide every 65 minutes, we will get this equation:

=1440/65

=22.15

Rounding this figure off, we get 22.

Thus, the number of times the hands of a clock will coincide is 22.

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