Subject: General Aptitude · Chapter: Area · Exam: 2002 · Marks: · Difficulty:
The length of a rectangle is decreased by $r \%$, and the breadth is increased by $(r+5) \%$. Find $r$, if the area of the rectangle is unaltered.
(a)5
(b)8
(c)10
(d)15
(e)20
Answer
Answer (as printed): E
Explanation
Let original length $=x$ and original breadth $=y$. Then, original area $=x y$. New area $=\left[\frac{(100-r)}{100} \times x\right]\left[\frac{(105+r)}{100} \times y\right]$ $=\left[\left(\frac{10500-5 r-r^{2}}{10000}\right) x y\right]$ $\therefore\left(\frac{10500-5 r-r^{2}}{10000}\right) x y=x y$ $\Leftrightarrow r^{2}+5 r-500=0 \Leftrightarrow(r+25)(r-20)=0 \Leftrightarrow r=20$.
Explanation as extracted from the printed page; notation may be imperfect.