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

Solution(By Examveda Team)

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