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GATE | GATE-CS-2014-(Set-2) | Question 65

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At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60o

(A)

6:22 am

(B)

6:27 am

(C)

6:38 am

(D)

6:45 am


Answer: (A)

Explanation:

Speed of the Hour hand = ( 360 degree ) / ( 12 * 60 minutes ) 
                       = 0.5 degree / minute.
Speed of the minute hand = ( 360 degree ) / ( 60 minutes ) 
                         = 6 degree / minute.

At 6 am, hour hand will point vertically downward to 6 in the clock, and minute hand will point vertically upward to 12 in the clock. ( Hence they are opposite with a gap of 180 degree between them). Now after t minutes, The angle between these two hands will be either of the below two:

(180 - 6t) + 0.5t, when the minute hand is 
                   behind the hour hand or,

6t - (180 + 0.5t), when the minute hand is 
                    ahead of hour hand,

Now the the question asks for angle of 60 degree.

Hence, 
(180 - 6t) + 0.5t = 60 , we get t = 21.8 minutes
and
6t - ( 180 + 0.5t ) = 60, we get t = 48 minutes

Hence the closest to answer is 22 minutes, i.e. 6.22 am. Hence answer is A.


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Last Updated : 28 Jun, 2021
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