Question

The angle (in degree) between the hour hand and the minute hand in a circular clock at $03:25$ hours is

• A. ${47.5}^{\circ }$
• B. ${52.5}^{\circ }$
• C. ${67.5}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is A ${47.5}^{\circ }$

We know that between $00:00$ and $03:25$ hours, time span covered in hours
$=3+\frac{25}{60}=\frac{41}{12}$
The angle traced by the hour hand in $12hrs$ is ${360}^{\circ }$
Angle traced by it in $\frac{41}{12}hrs$
$=\frac{{360}^{\circ }}{12}\times \frac{41}{12}=\frac{{410}^{\circ }}{4}={102.5}^{\circ }$

Angle traced by the minute hand in $60min$ is ${360}^{\circ }$
Angle traced by it in $25min$
$=\frac{{360}^{\circ }}{60}\times 25={150}^{\circ }$

Hence, the angle between the hour hand and the minute hand
$={150}^{\circ }-{102.5}^{\circ }={47.5}^{\circ }$