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1. 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. $120 %$

Solution:

Let original length = x and original breadth = y
Then, original area = xy
New length :

\begin{aligned} = \frac{160 x}{100} \\ = \frac{8 x}{5} \end{aligned}

Let the new breadth = z
Then,

\begin{aligned} \Rightarrow \frac{8 x}{5} \times z = x y \\ \Rightarrow z = \frac{5 y}{8} \end{aligned}

∴ Decrease in breadth :

\begin{aligned} = (\frac{3 y}{8} \times \frac{1}{y} \times 100) % \\ = 37 \frac{1}{2} % \end{aligned}

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