Question

The angle between the minute hand and the hour hand of a clock when the time is $7:20\text{a.m.}$ is

• A. ${120}^{\circ }$
• B. ${75}^{\circ }$
• C. ${90}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is D ${100}^{\circ }$

$7\text{hr}20min=7+\frac{20}{60}=\frac{22}{3}\text{hr}$
Angle traced by hour hand in $7\text{hr}20min={(\frac{22}{3}\times \frac{360}{12})}^{\circ }={220}^{\circ }$
Angle traced by the minute hand in $20min={(\frac{360}{60}\times 20)}^{\circ }={120}^{\circ }$

Hence, required angle between the two hands $={220}^{\circ }-{120}^{\circ }={100}^{\circ }$