At what time between 6 am and 7 am will the minute hand and the hour hand of a clock make an angle closest to 60°?
(A) 6:22 am
(B) 6:27 am
(C) 6:38 am
(D) 6:45 am
Explanation: Angular speed of hour hand = 360/12 = 30° per hour = 30/60 = 0.5° per minute.
Angular speed of minute hand = 360/60 = 6° per minute.
Relative speed of hour hand and minute hand = 6 – 0.5 = 5.5° per minute.
Angle between hour and minute hand at 6 AM = 180°.
To make an angle of 60°, total angular distance will be = 180° – 60° = 120°.
Time needed to cover angular distance of 120° by relative angular speed = 120°/5.5 = 21.81 minute.
Hence closest time to make an angle of 60° = 6:22 AM.
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