If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :

Answer: Option B

Let the original length and breadth of the rectangle be $$l$$ and b respectively.
Then,
Original area = $$lb$$
New length :
$$=110\%\text{ of }l=\frac{11}{10}l$$
New breadth :
$$=90\%\text{ of }b=\frac{9}{10}b$$
New area :
$$\begin{array}{rl}& =\left(\frac{11}{10}l\times \frac{9}{10}b\right)\\ & =\frac{99}{100}lb\end{array}$$
Decrease in area :
$$\begin{array}{rl}& =\left(lb-\frac{99}{100}lb\right)\\ & =\frac{lb}{100}\end{array}$$
∴ Decrease % :
$$\begin{array}{rl}& =\left(\frac{lb}{100}\times \frac{1}{1b}\times 100\right)\%\\ & =1\%\end{array}$$