Question

The angle between the minute hand and hour hand of the clock when the time is $09:30$ hours is

• A. ${105}^{\circ }$
• B. ${90}^{\circ }$
• C. ${135}^{\circ }$

Answer 1

The correct option is A ${105}^{\circ }$

To find: Angle between the minute hand and hour hand in a clock when the time is $09:30$ hours.
The sittuation can be represented by a diagram as:

Here, the required angle $=\angle BOA-\angle COA$
For hour hand $1$ Rotation $=12$ Hours
And for minute hand $1$ Rotation $=60$ minutes
$\Rightarrow$ Time taken to go from $00:00$ to $09:30$ hours
$=9+\frac{30}{60}=\frac{19}{2}$ hours.
Now, angle traced by hour hand in $12$ hours $={360}^{\circ }$
$\Rightarrow$Angle traced by hour hand in $19/2$ hours $=\frac{19}{2}\times \frac{{360}^{\circ }}{12}={285}^{\circ }=\angle BOA$
Now, for minute hand $1$ Rotation $=60$ minutes
Or angle traced by minute hand in $60$ minutes $={360}^{\circ }$
$\Rightarrow$ Angle traced by minute hand in $30$ minutes $=\frac{{360}^{\circ }}{60}\times 30={180}^{\circ }=\angle COA$
$\therefore$ Angle made by the minute hand and the hour hand when the time is $09:30$ hours $=\angle BOA-\angle COA$
$={285}^{\circ }-{180}^{\circ }={105}^{\circ }$