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 ?

Answer: Option B

Let the original length and breadth of the rectangle be l and b respectively
Then, original area = lb
New length = 120% of l = $$\frac{6l}{5}$$
New area = 150% of lb = $$\frac{3lb}{2}$$
New breadth :
$$\begin{array}{rl}& =\left(\frac{3lb}{2}\times \frac{5}{6l}\right)\\ & =\frac{5b}{4}\end{array}$$
Increase in breadth :
$$\begin{array}{rl}& =\left(\frac{5b}{4}-b\right)\\ & =\frac{b}{4}\end{array}$$
∴ Increase % :
$$\begin{array}{rl}& =\left(\frac{b}{4}\times \frac{1}{b}\times 100\right)\%\\ & =25\%\end{array}$$