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

Answer: Option C

$$\begin{array}{rl}& \text{Angle}\text{traced}\text{by}\text{hour}\text{hand}\text{in}\frac{21}{4}\text{hrs}\\ & ={\left(\frac{360}{12}\times \frac{21}{4}\right)}^{\circ }=157{\frac{1}{2}}^{\circ }\\ & \text{Angle}\text{traced}\text{by}\text{min}\text{.}\text{hand}\text{in}15\text{min}\\ & ={\left(\frac{360}{60}\times 15\right)}^{\circ }=90^{\circ }\\ & \therefore \text{Required}\text{angle}\\ & ={\left(157\frac{1}{2}\right)}^{\circ }-90^{\circ }\\ & =67{\frac{1}{2}}^{\circ }\end{array}$$