UPSC Prelims 2002 Q105: Science & Technology – Quantitative Aptitude
The time in the wall clock is 3.25; the acute angle between the hours hand and the minutes
hand is
- (a) 60°
- (b) 52 ½°
- (c) 47 ½°
- (d) 42°
Answer: (c) 47 ½°
Explanation
Acute angle between the clock hands at 3.25
| Hand | Position from 12 at 3:25 |
|---|---|
| Hour hand | 3 × 30 + 25 × 0.5 = 102.5° |
| Minute hand | 25 × 6 = 150° |
| Difference | 150 − 102.5 = 47.5° |
| Acute angle | 47 ½° |
At 3.25 the hour hand has moved 102.5° from the 12 mark and the minute hand is at 150°, so the angle between the hands of the clock is 47.5°, which is acute.
Answer: (c) 47 ½°.
Why each option is right or wrong
- (a) Incorrect. 60° would be the angle if the hour hand were exactly at the 3.
- (b) Incorrect. 52.5° ignores part of the hour hand's movement.
- (c) CORRECT. 150° − 102.5° = 47.5°.
- (d) Incorrect. 42° is not obtained from the standard formula.
Key point
Clock: the minute hand moves 6° a minute, the hour hand 0.5° a minute; angle = |30H − 5.5M|.
Remember
Angle = |30H − 5.5M| degrees.
Common mistakes
- Forgetting that the hour hand moves between the numbers.
- Using 90° minus 30° for the gap between the hands.
- Reporting the reflex angle instead of the acute angle.
Exam tip
|30 × 3 − 5.5 × 25| = |90 − 137.5| = 47.5°.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Clock)
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Clocks)