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How many times will minute hand and hour hand opposite in one day?









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Option(B) is correct

Eleven times in 12 hrs. The hands will be directly opposite each other at the following times: 

12:32 and 8/11 of a minute 
1:38 and 2/11 of a minute 
2:43 and 7/11 of a minute 
3:49 and 1/11 of a minute 
4:54 and 6/11 of a minute 
7:05 and 5/11 of a minute 
8:10 and 10/11 of a minute 
9:16 and 4/11 of a minute 
10:21 and 9/11 of a minute 
11:27 and 3/11 of a minute.

Therefore, the hands of the clock will be opposite to each other 22 times.

Edit: Thank you, Robin for providing an alternative solution in the comments.

(1) Comment(s)


Here is another method to solve the problem:

The minute hand travels an angular distance of 360 degrees in 60 minutes. So, it covers 6 degrees in one minute.

The hour hand covers $2\times 360^\circ$ in 24 hours, i.e 1440 minutes. So, in one minute, it covers $\dfrac{1440}{720} = \left(\dfrac{1}{2}\right)^\circ$.

Difference in angular distance travelled by the minute hand and the hour hand in one minute is thus $6-\dfrac{1}{2} = \dfrac{11}{2}$ degrees. So, on a full rotation $(360^\circ)$, any similar event between them will be repeated every $\dfrac{360}{(11/2} = 65 \dfrac{5}{11}$ minutes.

In twenty four hours, i.e. $24 \times 60 = 1440$ minutes, the number of times angle between the minute hand and hour hand will be same, can be calculated by dividing 1440 minutes with this value, thus,


So, $180^\circ$ angle (event of opposition) will be obtained $\textbf{= 22 times.}$