Question

The angle between hands of a clock when the time is $4.25AM$ is:

• A. $17{\frac{1}{2}}^{\circ }$
• B. $14{\frac{1}{2}}^{\circ }$
• C. $13{\frac{1}{2}}^{\circ }$
• D. $12{\frac{1}{2}}^{\circ }$

Answer 1

Answer: (A)

$17{\frac{1}{2}}^{\circ }$

The minute hand of the clock will be at $\frac{{25}^o}{{60}^o}\times {360}^o=150$

The hour hand of the clock will be between 4 and 5 in ratio 25:35.

Angle at $4$ AM $={120}^o$ and angle at $5$ AM $={150}^o$

Angle at $4:25$ AM $=\frac{35\times 120+150\times 25}{35+25}=132\frac{1^o}{2}$

Angle between the two hands $={150}^o-132\frac{1^o}{2}=17\frac{1^o}{2}$