Question

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

• A. 20
• B. 30
• C. 10
• D. 80

Answer 1

The correct option is C 10

The speed of hour hand is ( $30$ degree per hour) ${0.5}^{\circ }$ per minute.

The speed of minute hand is ($360$ degree per hour) $6^{\circ }$ per minute.

Relative to hour hand the speed of minute hand is $6-0.5={5.5}^{\circ }$per minute.

At $4$ O clock , hour hand is at $4$ and minute hand is at $12$.

Angle between them is ${120}^{\circ }$.

Keeping hour hand at $4$ , minute hand moves $20\times 5.5={110}^{\circ }$, in $20$ minutes.

Angle between them is ${120}^{\circ }-{110}^{\circ }={10}^{\circ }$.