SSC CGL 2022 PYQ — Question 71

The correct answer is Option 1.i.e. 13.4%.

Length of original rectangle = x

The breadth of original rectangle = y

Then, Area of Original Rectangle = xy

Length of New Rectangle

$\begin{aligned} & =>x+\frac{5 x}{100} \\ & =>x+\frac{x}{20} \\ & =>\frac{21 x}{20}\end{aligned}$

Breadth of New Rectangle

$\begin{aligned} & =>y+\frac{8 y}{100} \\ & =>y+\frac{2 y}{25} \\ & =>\frac{27 y}{25}\end{aligned}$

Now,

Area of New Rectangle  $=>\frac{21 x}{20} \times \frac{27 y}{25}=\frac{567 x y}{500}$

Increase in area

$\begin{aligned} & =>\frac{567 x y}{500}-x y \\ & =>\frac{567 x y-500 x y}{500} \\ & =>\frac{67 x y}{500} \end{aligned}$

Percent Increase 

$\begin{aligned} & =>\frac{\frac{67 x y}{50 y}}{x y} \times 100 \\ & =>\frac{67 x y}{500} \times \frac{1}{x y} \times 100 \\ & =>\frac{67}{5}=13.4 \end{aligned}$

Percent Increase = 13.4%