Question

Angle between the hour and minute hand of a clock at 11 : 15 is -

• A. ${90}^{\circ }$
• B. ${112.5}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is B ${112.5}^{\circ }$

In 12 hours, hour hand gains an angle of ${360}^{\circ }$. In $11\frac{1}{4}$ hours, hour hand gains an angle
$=\frac{360}{12}\times \frac{45}{4}=\frac{675}{2}={337.5}^{\circ }$
In 60 minutes, minute hand gains an angle $={360}^{\circ }$
In 15 minutes, minute hand gains an angle $=\frac{{360}^{\circ }}{{60}^{\circ }}\times 15={90}^{\circ }$

At 11:15, the difference between the minute hand and hour hand of a clock is $={90}^{\circ }+({360}^{\circ }-{337.5}^{\circ })$
$={112.5}^{\circ }$