If the length of a rectangle is increased by 50% and breadth is decreased by 25%, what is the percentage change in its area ?

Answer: Option A

Let the original length and breadth of the rectangle be $$l$$ and b respectively
New length :
$$=150\%\text{ of }l=\frac{3l}{2}$$
New breadth :
$$=75\%\text{ of }b=\frac{3b}{4}$$
Original area = $$lb$$
New area :
$$\begin{array}{rl}& =\left(\frac{3l}{2}\times \frac{3b}{4}\right)\\ & =\frac{9lb}{8}\end{array}$$
Increase in area :
$$\begin{array}{rl}& =\left(\frac{9lb}{8}-lb\right)\\ & =\frac{lb}{8}\end{array}$$
∴ Increase % :
$$\begin{array}{rl}& =\left(\frac{lb}{8}\times \frac{1}{lb}\times 100\right)\%\\ & =12.5\%\end{array}$$