Question

The length and breadth of a rectangle field are increased, the area increased by $50$%. If the length increased by $20$%, by what percentage was breadth increased?

• A. 25%
• B. 30%
• C. 20%
• D. Data in adequate

Answer 1

Answer: (A)

25%

Let

$\begin{array}{c}length=l\\ breadth=b\\ Area=l\times b\end{array}$

Now increased in length by 50 %

$L=l+l\times \frac{20}{100}=l+\frac{l}{5}=\frac{6l}{5}$

increased in Area by 50 %

$A=lb+lb\times \frac{50}{100}$

Let increased in breadth =B

Now $L\times B=\frac{3lb}{2}$

$\begin{array}{c}\frac{bl}{5}\times B=\frac{3l\times b}{2}\\ B=\frac{5}{4}b\end{array}$

let increase in x

$\%x=\frac{\left(\frac{5}{4}-1\right)b}{b}\times 100$

$\%x=\frac{1}{4}\times 100$

$\%x=25\%$