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 :

Answer: Option D

Let original length = x and original breadth = y
Then,
Original area = xy
New area :
$$\begin{array}{rl}& =\left[\frac{\left(100-r\right)}{100}\times x\right]\left[\frac{\left(105+r\right)}{100}\times y\right]\\ & =\left[\left(\frac{10500-5r-r^2}{10000}\right)xy\right]\\ & \therefore \left(\frac{10500-5r-r^2}{10000}\right)xy=xy\\ & \Rightarrow r^2+5r-500=0\\ & \Rightarrow \left(r+25\right)\left(r-20\right)=0\\ & \Rightarrow r=20\end{array}$$