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# The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{original}\phantom{\rule{thinmathspace}{0ex}}\text{length}=x\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\\ & \text{Original}\phantom{\rule{thinmathspace}{0ex}}\text{breadth}=y\\ & \text{Original}\phantom{\rule{thinmathspace}{0ex}}\text{area}=xy\\ & \text{New}\phantom{\rule{thinmathspace}{0ex}}\text{length}=\frac{x}{2}\\ & \text{New}\phantom{\rule{thinmathspace}{0ex}}\text{breadth}=3y\\ & \text{New}\phantom{\rule{thinmathspace}{0ex}}\text{area}=\left(\frac{x}{2}×3y\right)=\frac{3}{2}xy\\ & \therefore \text{Increase}\phantom{\rule{thinmathspace}{0ex}}\mathrm{%}=\left(\frac{1}{2}xy×\frac{1}{xy}×100\right)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=50\mathrm{%}\end{array}$