The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :

Solution(By Examveda Team)

Let length = $$l$$ metres and breadth = b metres
Then, original area = (lb) m²
New length :
$$\eqalign{ & = \left( {140\% {\text{ of }}l} \right)m \cr & = \left( {\frac{{140}}{{100}} \times l} \right)m \cr & = \frac{{7l}}{5}m \cr} $$
New breadth :
$$\eqalign{ & = \left( {130\% {\text{ of }}b} \right)m \cr & = \left( {\frac{{130}}{{100}} \times b} \right)m \cr & = \frac{{13l}}{{10}}m \cr} $$
New area :
$$\eqalign{ & = \left( {\frac{{7l}}{5} \times \frac{{13b}}{{10}}} \right){m^2} \cr & = \left( {\frac{{91lb}}{{50}}} \right){m^2} \cr} $$
Increase :
$$\eqalign{ & = \left( {\frac{{91lb}}{{50}} - lb} \right) \cr & = \frac{{41}}{{50}}lb \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{41}}{{50}} \times lb \times \frac{1}{{lb}} \times 100} \right)\% \cr & = 82\% \cr} $$