Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
If the length and breadth of a rectangular field are increased, the area increases by 50\%. If the increase in length was 20\%, by what percentage was the breadth increased?
(a)20\%
(b)25\%
(c)30\%
(d)Date inadequate
(e)None of these
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 $=120 \%$ of $l=\frac{6}{5} l$. New area $=150 \%$ of $l b=\frac{3 l b}{2}$. New breadth $=\left(\frac{3 l b}{2} \times \frac{5}{6 l}\right)=\frac{5 b}{4}$. Increase in breadth $=\left(\frac{5 b}{4}-b\right)=\frac{b}{4}$. $$\text { ∴ } \text { Increase } \%=\left(\frac{b}{4} \times \frac{1}{b} \times 100\right) \%=25 \%$$
Explanation as extracted from the printed page; notation may be imperfect.