If each side of a square is increased by 10%, its area will be increased by :

Answer: Option B

Let the original length of sides be x
Then, new length :
$$\begin{array}{rl}& =\left(110\%\text{ of }x\right)\\ & =\frac{11x}{10}\end{array}$$
Original area $$x^2$$
New area :
$$\begin{array}{rl}& ={\left(\frac{11x}{10}\right)}^2\\ & =\frac{121x^2}{100}\end{array}$$
Increase in area :
$$\begin{array}{rl}& =\left(\frac{121x^2}{100}-x^2\right)\\ & =\frac{21x^2}{100}\end{array}$$
∴ Increase % :
$$\begin{array}{rl}& =\left(\frac{21x^2}{100}\times \frac{1}{x^2}\times 100\right)\%\\ & =21\%\end{array}$$