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

Let the original length and breadth be l and b respectively. Hence initial area is $lb$

hence the new length is $l(1+\frac{20}{100})=l\left(\frac{120}{100}\right)=\frac{6l}{5}$

hence new breadth will be $b(1-\frac{20}{100})=b\left(\frac{80}{100}\right)=\frac{4b}{5}$

hence new area is $\frac{6l}{5}\times \frac{4b}{5}=\frac{24lb}{25}$

Hence the area decreases .

Decrease in area $=lb-\frac{24lb}{25}=\frac{lb}{25}$

hence % decrease $=\frac{Change}{Initial}\times 100=\frac{\frac{lb}{25}}{lb}\times 100=\frac{lb\times 100}{25\times lb}=4\%$

Hence the area decreases by 4%