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 :

Answer: Option D

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