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At what time between 3 and 4 Oâ€™clock will the hour and minute hand of a clock be at an angle of 60̊ with each other?

A.	3hrs 27*3/11 min	B.	3 hrs 5*5/11 min
C.	(A) or (B)	D.	None of these

Answer and Explanation

Answer:(A) or (B)

Explanation:
Let at 3 hrs M min the angle between H.H and M.H is 60̊
Case 1: H.H is before M.H
11/2 Ã— M â€“ 30 Ã— H = 60̊
11/2 Ã— M â€“ 30 Ã— 3 = 60̊
11/2 Ã— M = 90̊ + 60̊
M = 150 Ã— 2/ 11 = 300/11 = 27 3/11
At 3 hrs 27 3/11 min the angle between the hands in 60̊
Case II: M.H. is before H.H
30 Ã— H â€“ 11/2 Ã— M = 60̊
30 Ã— 3 = 11/2 Ã— M =60̊.
M = 30Ã—2 / 11 = 60/11 = 5 5/11 at 3 hrs 5 5/11 min the angle between the hands is 60̊

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