How many times do the hands of a clock make an angle of in hours?

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answer is D.

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Detailed Solution

First of all, we will draw a clock for a better understanding of the clock properties:
Now, we will suppose that both the hour and minute hand is on twelve. When the minute hand will come to a point at three and nine, it will make an angle of

with the hour hand.
So, we can say that in one hour the minute hand and hour hand overtakes itself twice to give an angle of

Similarly, for the next hour, again it will form the right angle two times. This property will repeat till both the hour and minute hand again comes at point twelve.
So, the total number of

angles in the

hours of a day equals to

, because twelve repeats itself two times in these

hours.
⇒Total number of

angle in

hours

Now, for the next

hours, the total number of

angles will be equals to

.
⇒Total number of

angle in next

hours
Again, for the next