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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