Subject: General Aptitude · Chapter: Area · Exam: 2006 · Marks: · Difficulty:
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
(a)35\%
(b)42\%
(c)62\%
(d)82\%
Answer
Answer (as printed): D
Explanation
Let length $=l$ metres and breadth $=b$ metres. Then, original area $=(l b) \mathrm{m}^{2}$. New length $=(140 \%$ of $l) \mathrm{m}=\left(\frac{140}{100} \times l\right) \mathrm{m}=\frac{7 l}{5} \mathrm{m}$. New breadth $=(130 \%$ of $b) \mathrm{m}=\left(\frac{130}{100} \times b\right) \mathrm{m}=\frac{13 b}{10} \mathrm{m}$. New area $=\left(\frac{7 l}{5} \times \frac{13 b}{10}\right)=\left(\frac{91}{50} l b\right) \mathrm{m}^{2}$. Increase $=\left(\frac{91}{50} l b-l b\right)=\frac{41}{50} l b$. $\therefore \quad$ Increase $\%=\left(\frac{41}{50} \times l b \times \frac{1}{l b} \times 100\right) \%=82 \%$.