Question

At 03:40, the hour hand and the minute hand of a clock form an angle of

• A. ${120}^{\circ }$
• B. ${125}^{\circ }$
• C. ${130}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is C ${130}^{\circ }$

Angle traced by hour hand in 12 hours $={360}^{\circ }$.
Angle traced by it in $\frac{11}{3}$ hrs $={(\frac{360}{12}\times \frac{11}{3})}^{\circ }={110}^{\circ }$
Angle traced by minute hand in 60 minute $={360}^{\circ }$.
Angle traced by it in 40 minute $={(\frac{360}{60}\times 40)}^{\circ }={240}^{\circ }$.
$\therefore$ Required angle $(240-110{)}^{\circ }={130}^{\circ }$.