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# The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Angle}\phantom{\rule{thinmathspace}{0ex}}\text{traced}\phantom{\rule{thinmathspace}{0ex}}\text{by}\phantom{\rule{thinmathspace}{0ex}}\text{hour}\phantom{\rule{thinmathspace}{0ex}}\text{hand}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\frac{13}{3}\phantom{\rule{thinmathspace}{0ex}}\text{hrs}\\ & ={\left(\frac{360}{12}×\frac{13}{3}\right)}^{\circ }={130}^{\circ }\\ & \text{Angle}\phantom{\rule{thinmathspace}{0ex}}\text{traced}\phantom{\rule{thinmathspace}{0ex}}\text{by}\phantom{\rule{thinmathspace}{0ex}}\text{min}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{hand}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\text{20}\phantom{\rule{thinmathspace}{0ex}}\text{min}\\ & ={\left(\frac{360}{60}×20\right)}^{\circ }={120}^{\circ }\\ & \therefore \text{Required}\phantom{\rule{thinmathspace}{0ex}}\text{angle}\\ & ={\left(130-120\right)}^{\circ }\\ & ={10}^{\circ }\end{array}$