What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
- (a) 12·5°
- (b) 15°
- (c) 17·5° ✓ UPSC's answer
- (d) 20°
Why the answer is (c)
• The hour hand moves 0.5° per minute, so at 4:25 it is at 4 * 30° + 25 * 0.5° = 132.5° from the 12 o'clock position.
• The minute hand moves 6° per minute, so at 25 minutes it is at 25 * 6° = 150° from the 12 o'clock position.
• The absolute difference between the two positions is |150° - 132.5°| = 17.5°.
• Since 17.5° is less than 180°, it is the smaller angle between the hands.
• Therefore, the correct angle is 17.5°, which corresponds to option (c).
Why the other options are wrong
- (a) 12·5°
- 12.5° is incorrect because it does not account for the hour hand's movement of 12.5° past the 4 o'clock mark.
- (b) 15°
- 15° is incorrect because it assumes the hour hand remains exactly at the 4 o'clock position (120°) rather than moving to 132.5°.
- (d) 20°
- 20° is incorrect because it results from an arithmetic error in calculating the difference between the minute and hour hand positions.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.