Question

On increasing the length of a rectangle by 20% and decreasing its breadth by 20%, what is the change in its area?
(a) 20% increase
(b) 20% decrease
(c) No change
(d) 4% decrease

Answer 1

(d) 4% decrease

Let:
Length$=x$
breadth$=y$
Area$=xy$

Now,
New length$=x+20\%x=x+\frac{1}{5}x=\frac{6}{5}x$

New breadth$=y-20\%y=y-\frac{1}{5}y=\frac{4}{5}y$

New area$=\frac{6}{5}x\times \frac{4}{5}y=\frac{24}{25}xy$

Difference in the areas$=xy-\frac{24}{25}xy=\frac{1}{25}xy$

Difference in percentage$=\left[\left({\displaystyle \frac{\frac{1}{25}xy}{xy}}\right)\times 100\right]\%=4\%$