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} $