Question

The acute angle between the minute and hour hands when the time is 3 hours and 10 minutes is

• A. $\frac{7\pi }{36}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{36}$
• D. $\frac{5\pi }{36}$

Answer 1

Answer: (A)

Angle traced by the hour hand in 12 hrs = $360^{\circ }$
Angle traced by it in 3 hrs 10 mins i.e., $\frac{19}{6}$ hrs
$=\frac{19}{6}\times \frac{360}{12}=95^{\circ }$
Angle traced by it in 10 mins $=\frac{360}{60}\times 10=60^{\circ }$
Required angle $=95-60=35=\frac{7\pi }{36}$