Subject: General Aptitude · Chapter: Area · Exam: 2006 · Marks: · Difficulty:
The length of a rectangle is increased by 60\%. By what percent would the width have to be decreased so as to maintain the same area?
(a)$37 \frac{1}{2} \%$
(b)60\%
(c)75\%
(d)120\%
Answer
Answer (as printed): A
Explanation
Let original length $=x$ and original breadth $=y$. Then original area $=x y$. New length $=\frac{160 x}{100}=\frac{8 x}{5}$. Let new breadth $=z$. Then, $\frac{8 x}{5} \times z=x y \Rightarrow z=\frac{5 y}{8}$. ∴ Decrease in breadth $=\left(\frac{3 y}{8} \times \frac{1}{y} \times 100\right) \%=37 \frac{1}{2} \%$.
Explanation as extracted from the printed page; notation may be imperfect.