Question

The acute angle between the hour hand and minute hand of a clock when the time is $5\, hours$ and $40\, minute$ is

• A. $\frac{\pi}{2}$
• B. $\frac{13 \pi}{36}$
• C. $\frac{5 \pi}{18}$
• D. $\frac{7 \pi}{18}$

Answer 1

Answer: (D)

For minute hand 60 minutes =$ 360^\circ $
40 minutes = $ \frac{360^\circ }{60} \times 40 = 240^\circ $ and for hour hand
1 hr = 60 minutes = $30^\circ $
40 minutes = $ \frac{30^\circ }{60} \times 40 = 20^\circ $
$ \therefore $ For 5 hr 40 min.= $ 30^\circ \times 5 + 20^\circ = 170^\circ $.
Hence, required angle = $240^\circ - 170^\circ = 70^\circ $
$ = 70^\circ \times \frac{\pi}{180^\circ}= \frac{7 \pi}{18}$