The length of a rectangle is decreased by $20\%$ and breadth increased by $20\%.$ The area will

The correct option is A: decrease by $4\%$

Let original length $=l$

And, original breadth $=b$

Original area of the rectangle $=l\times b=lb$

When the length of a rectangle is decreased by $20\%$ and breadth increased by $20\%$. then

New Length $=l-20\%l=l-0.20l=0.80l$

And, New breadth $=b+20\%=b+0.20b=1.20b$

New area of rectangle $=0.80l\times 1.20b$

Percentage change in area $=\frac{\text{Change in area}}{\text{Original area}}\times 100\%$

$=\frac{(0.80l\times 1.20b)-lb}{lb}\times 100\%$

$=\frac{0.80\times 1.20-1}{1}\times 100\%$

$=(0.96-1)\times 100\%$

$=-4\%$