Question

The angle between the minute hand and the hour hand of a clock when the time is 4:20 is:

• A. 0°
• B. 5°
• C. 10°
• D. 20°
• E. 15°

Hint:

Formula: $\theta = |30H - 5.5M|$. For 4:20: $|30(4) - 5.5(20)| = |120 - 110| = 10^\circ$.

Answer 1

The Correct Option is C

Step 1: Analyse options.
- At 4:20, the minute hand is exactly on the 4 ($20 \text{ minutes} \times 6^\circ/\text{min} = 120^\circ$ from 12). - The hour hand has moved from 4 toward 5. - Angle moved by hour hand in 20 mins = $20 \times 0.5^\circ/\text{min} = 10^\circ$. - Since the minute hand is at the 4 mark, the difference is exactly the displacement of the hour hand.
Step 2: Conclusion.
The angle is 10°. Final Answer: (c) 10°