Question

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

• A. $0^\circ$
• B. $10^\circ$
• C. $5^\circ$
• D. $20^\circ$

Hint:

Remember the hour hand moves continuously, so always add $0.5^\circ$ per minute to its base $30^\circ \times H$ position.

Answer 1

The Correct Option is B

Step 1: Formula for hand positions.
- Minute hand position (in degrees from 12 o’clock) $= 6 \times M$.
- Hour hand position (in degrees from 12 o’clock) $= 30 \times H + 0.5 \times M$.
Here $H$ = hour, $M$ = minutes. Step 2: Find the positions at 4:20.
Minute hand: $6 \times 20 = 120^\circ$.
Hour hand: $30 \times 4 + 0.5 \times 20 = 120 + 10 = 130^\circ$. Step 3: Difference between hands.
$|130^\circ - 120^\circ| = 10^\circ$. \[ \boxed{10^\circ\ \text{(Option (b)}} \]