Angle between the hands — Aptitude Question
Angle between the hands: What is the angle between the hour and minute hands of a clock at 3:30? Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the angle between the hour and minute hands of a clock at 3:30?
Options
- 70°
- 75°
- 80°
- 90°
Show the answer and the worked solution
Correct answer: B. 75°
Worked solution
- Minute hand at 30 min = 30 × 6 = 180°.
- Hour hand = 30 × 3 + 0.5 × 30 = 90 + 15 = 105°.
- Angle = 180 − 105 = 75°.
Answer: 75°.
The idea
Angle = |30H − 5.5M|. If it exceeds 180°, subtract from 360°. The 0.5° per minute drift of the hour hand is what most candidates forget.
Shortcut. At 3:30 the hour hand is halfway between 3 and 4 and the minute hand is on 6: 2½ hour-gaps × 30° = 75°.
Common trap. 90° — leaving the hour hand on the 3; in 30 minutes it moves 15° towards the 4.