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

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 :
$$\eqalign{ & = \left( {\frac{{3l}}{2} \times \frac{{3b}}{4}} \right) \cr & = \frac{{9lb}}{8} \cr} $$
Increase in area :
$$\eqalign{ & = \left( {\frac{{9lb}}{8} - lb} \right) \cr & = \frac{{lb}}{8} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{lb}}{8} \times \frac{1}{{lb}} \times 100} \right)\% \cr & = 12.5\% \cr} $$