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 ?

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 :
$$\eqalign{ & = \left( {\frac{{3lb}}{2} \times \frac{5}{{6l}}} \right) \cr & = \frac{{5b}}{4} \cr} $$
Increase in breadth :
$$\eqalign{ & = \left( {\frac{{5b}}{4} - b} \right) \cr & = \frac{b}{4} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{b}{4} \times \frac{1}{b} \times 100} \right)\% \cr & = 25\% \cr} $$