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1. At what angle the hands of a clock are inclined at 15 minutes past 5?

A. $58 {\frac{1}{2}}^{\circ}$

B. $64^{\circ}$

C. $67 {\frac{1}{2}}^{\circ}$

D. $72 {\frac{1}{2}}^{\circ}$

Solution:

\begin{aligned} Angle traced by hour hand in \frac{21}{4} hrs \\ = {(\frac{360}{12} \times \frac{21}{4})}^{\circ} = 157 {\frac{1}{2}}^{\circ} \\ Angle traced by min . hand in 15 min \\ = {(\frac{360}{60} \times 15)}^{\circ} = 90^{\circ} \\ ∴ Required angle \\ = {(157 \frac{1}{2})}^{\circ} - 90^{\circ} \\ = 67 {\frac{1}{2}}^{\circ} \end{aligned}

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