The length of a rectangle is increased by 25% and the breadth is decreased by 20%. What is the percentage change in area?

Let the initial length and breadth of the rectangle be $$L$$ and $$B$$.

We are told that the length is increased by 25% and the breadth is decreased by 20%. So, the new length and breadth become 

Length $$L\left(1\ +\dfrac{25}{100}\right)\ =\ \dfrac{5}{4}L$$

Breadth $$=\ B\left(1\ -\ \dfrac{20}{100}\right)\ =\ \dfrac{4}{5}B$$

Initial Area $$=\ L\times\ B$$

Final Area $$=\ \dfrac{5}{4}L\times\ \dfrac{4}{5}B\ =\ L\ \times\ B$$

We can see that there is no change in the Area. So the percentage change in area is 0%.

Hence, the correct answer is option A.