The length of a rectangle is increased by 60%. By what percent would the width have to be decreased so as to maintain the same area ?

A. $$37\frac{1}{2}\% $$

B. $$60\% $$

C. $$75\% $$

D. $$120\% $$

Answer: Option A

Solution(By Examveda Team)

Let original length = x and original breadth = y
Then, original area = xy
New length :
$$\eqalign{ & = \frac{{160x}}{{100}} \cr & = \frac{{8x}}{5} \cr} $$
Let the new breadth = z
Then,
$$\eqalign{ & \Rightarrow \frac{{8x}}{5} \times z = xy \cr & \Rightarrow z = \frac{{5y}}{8} \cr} $$
∴ Decrease in breadth :
$$\eqalign{ & = \left( {\frac{{3y}}{8} \times \frac{1}{y} \times 100} \right)\% \cr & = 37\frac{1}{2}\% \cr} $$