It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________. A. 0 degrees B. 7.5 degrees C. 15 degrees D. 22.5 degrees

GATE 2020 · General Aptitude · Clock Time · medium

Answer: The angle between the hour and minute hand at 3:15 (quarter past three) is 7.5 degrees. Answer: B. 7.5 degrees.

1. Apply the clock angle formula: H = 3, t = 15 minutes past 3. angle = |30 x 3 - 5.5 x 15| = |90 - 82.5| = |7.5| = 7.5 degrees.
2. Verify using individual positions: theta_hr = 30 x 3 + 0.5 x 15 = 90 + 7.5 = 97.5 deg. theta_min = 6 x 15 = 90 deg. Angle = |97.5 - 90| = 7.5 degrees.