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1. If the length and breadth of a rectangular field are increased, the area increases by 50%. If the increase in length was 20 %, by what percentage was the breadth increased ?

A. 20%

B. 25%

C. 30%

D. Data inadequate

Solution:

Let the original length and breadth of the rectangle be l and b respectively
Then, original area = lb
New length = 120% of l =

\frac{6 l}{5}

New area = 150% of lb =

\frac{3 l b}{2}

New breadth :

\begin{aligned} = (\frac{3 l b}{2} \times \frac{5}{6 l}) \\ = \frac{5 b}{4} \end{aligned}

Increase in breadth :

\begin{aligned} = (\frac{5 b}{4} - b) \\ = \frac{b}{4} \end{aligned}

∴ Increase % :

\begin{aligned} = (\frac{b}{4} \times \frac{1}{b} \times 100) % \\ = 25 % \end{aligned}

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