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At what time between 3 and 4 O’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 × M – 30 × H = 60̊
11/2 × M – 30 × 3 = 60̊
11/2 × M = 90̊ + 60̊
M = 150 × 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 × H – 11/2 × M = 60̊
30 × 3 = 11/2 × M =60̊.
M = 30×2 / 11 = 60/11 = 5 5/11 at 3 hrs 5 5/11 min the angle between the hands is 60̊

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