Question

The angle between the minute hand and the hour hand of a clock when the time is $4:20$ P.M., is

• A. $0^{\circ }$
• B. $5^{\circ }$
• C. ${10}^{\circ }$
• D. $7^{\circ }$

Answer 1

The correct option is C ${10}^{\circ }$

Given time : $4:20=4$ hr $20$ min $=\frac{13}{3}$ hrs
We know that minute hand traces an angle of ${360}^{\circ }$ in one hour.
Hence, angle traced by minute hand in $20$ min $={(\frac{360}{60}\times 20)}^{\circ }={120}^{\circ }$

We know that hour hand traces an angle of ${360}^{\circ }$ in $12$ hours.
Hence, angle traced by hour hand in $\frac{13}{3}$ hrs $={(\frac{360}{12}\times \frac{13}{3})}^{\circ }={130}^{\circ }$
$\therefore$ Required angle $={130}^{\circ }-{120}^{\circ }={10}^{\circ }$