Subject: General Aptitude · Chapter: Area · Exam: 2010 · Marks: · Difficulty:
If the length of a rectangle is increased by 10\% and its breadth is decreased by 10\%, the change in its area will be
(a)1\% increase
(b)1\% decrease
(c)10\% increase
(d)No change
Answer
Answer (as printed): B
Explanation
Let the original length and breadth of the rectangle be $l$ and $b$ respectively. Then, original area $=l b$. New length $=110 \%$ of $l=\frac{11}{10} l$; New breadth $=90 \%$ of $b=\frac{9}{10} b$. New area $=\left(\frac{11}{10} l \times \frac{9}{10} b\right)=\frac{99}{100} l b$. Decrease in area $=\left(l b-\frac{99}{100} l b\right)=\frac{l b}{100}$. ∴ Decrease $\%=\left(\frac{l b}{100} \times \frac{1}{1 b} \times 100\right) \%=1 \%$.
Explanation as extracted from the printed page; notation may be imperfect.