Clock Angle at Half Past – UGC NET Question

At 3:30, the minute hand is at 30 minutes, which is 30 × 6 = 180 degrees from 12 o’clock, since each minute corresponds to 6 degrees. The hour hand moves 30 degrees per hour plus 0.5 degrees per minute. By 3:30 it has moved 3 × 30 = 90 degrees for three full hours and 0.5 × 30 = 15 degrees for the extra 30 minutes, totalling 105 degrees. The angle between the two hands is |180 − 105| = 75 degrees, so 75 degrees is the correct answer.

Option A:
Option A, 45 degrees, might be chosen by wrongly assuming that the hour hand stays fixed exactly at 3 when the minute hand is at 6, but in reality the hour hand has advanced halfway towards 4 by 3:30.

Option B:
Option B, 60 degrees, would correspond to some other specific times but does not result from the correct calculation of the hands’ positions at 3:30. It underestimates the actual separation once the hour hand’s extra movement is considered.

Option C:
Option C carefully computes both hands’ positions using their respective angular speeds and then subtracts to find the included angle. This process gives 75 degrees, matching the standard result for this clock-angle case.

Option D:
Option D, 90 degrees, assumes that the hands are perpendicular at 3:30, but they are exactly perpendicular at 3:00; by 3:30 the hour hand has moved ahead, so the angle is less than 90 degrees.