Subject: General Aptitude · Chapter: Area · Exam: 2004 · Marks: · Difficulty:
If each side of a square is increased by 10\%, its area will be increased by
(a)10\%
(b)21\%
(c)44\%
(d)100\%
Answer
Answer (as printed): B
Explanation
Let original length of side be $x$. Then, new length $=(110 \%$ of $x)=\frac{11 x}{10}$. Original area $=x^{2}$ New area $=\left(\frac{11 x}{10}\right)^{2}=\frac{121 x^{2}}{100}$. Increase in area $=\left(\frac{121 x^{2}}{100}-x^{2}\right)=\frac{21 x^{2}}{100}$. ∴ $\quad$ Increase $\%=\left(\frac{21 x^{2}}{100} \times \frac{1}{x^{2}} \times 100\right) \%=21 \%$.
Explanation as extracted from the printed page; notation may be imperfect.