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# The reflex angle between the hands of a clock at 10.25 is:

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Angle}\phantom{\rule{thinmathspace}{0ex}}\text{traced}\phantom{\rule{thinmathspace}{0ex}}\text{by}\phantom{\rule{thinmathspace}{0ex}}\text{hour}\phantom{\rule{thinmathspace}{0ex}}\text{hand}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\frac{125}{12}hrs\\ & ={\left(\frac{360}{12}×\frac{125}{12}\right)}^{\circ }=312\frac{{1}^{\circ }}{2}\\ & \text{Angle}\phantom{\rule{thinmathspace}{0ex}}\text{traced}\phantom{\rule{thinmathspace}{0ex}}\text{by}\phantom{\rule{thinmathspace}{0ex}}\text{minute}\phantom{\rule{thinmathspace}{0ex}}\text{hand}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\text{25}\phantom{\rule{thinmathspace}{0ex}}min\\ & ={\left(\frac{360}{60}×25\right)}^{\circ }={150}^{\circ }\\ & \therefore \text{Reflex}\phantom{\rule{thinmathspace}{0ex}}\text{angle}\\ & ={360}^{\circ }-{\left(312\frac{1}{2}-150\right)}^{\circ }\\ & ={360}^{\circ }-162\frac{{1}^{\circ }}{2}\\ & =197\frac{1}{2}\end{array}$

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