On increasing the length of a rectangle by 20% and decreasing its breadth by 20%, what is the change in its area?
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
Solution:
(d) 4% decrease
Let:
Length $=x$
breadth $=y$
Area $=x y$
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 $=\frac{6}{5} x \times \frac{4}{5} y=\frac{24}{25} x y$
Difference in the areas $=x y-\frac{24}{25} x y=\frac{1}{25} x y$
Difference in percentage $=\left[\left(\frac{\frac{1}{25} x y}{x y}\right) \times 100\right] \%=4 \%$