Subject: General Aptitude · Chapter: Area · Exam: 2010 · Marks: · Difficulty:
If the length of a rectangle is increased by 50\% and breadth is decreased by 25\%, what is the percentage change in its area?
(a)12.5\% increase
(b)10\% increase
(c)25\% increase
(d)20\% decrease
Answer
Answer (as printed): A
Explanation
Let the original length and breadth of the rectangle be $l$ and $b$ respectively. New length $=150 \%$ of $l=\frac{3}{2} l$; New breadth $=75 \%$ of $b=\frac{3}{4} b$. Original area $=l b$. New area $=\left(\frac{3}{2} l \times \frac{3}{4} b\right)=\frac{9}{8} l b$. Increase in area $=\left(\frac{9}{8} l b-l b\right)=\frac{l b}{8}$. ∴ Increase \% $=\left(\frac{l b}{8} \times \frac{1}{l b} \times 100\right) \%=12.5 \%$.
Explanation as extracted from the printed page; notation may be imperfect.