Question

The length of a given rectangle is increased by 20% and the breadth is decreased by 20% then the area

• A. remains the same
• B. Increases by 5%
• C. decreases by 5%
• D. decreases by 4%

Answer 1

The correct option is D decreases by 4%

Let the length of rectangle is x and width of rectangle is y

Then area of rectangle=$length\times width=x\times y=xy$

If length increased by 20% then new length =$\frac{x\times 120}{100}=\frac{6x}{5}$

If width decreased by 20% then new width =$\frac{y\times 80}{100}=\frac{4y}{5}$

Then area of new rectangle =$\frac{6x}{5}\times \frac{4y}{5}=\frac{24xy}{25}$

Then area rectangle decreased=$xy-\frac{24xy}{25}=\frac{25xy-24xy}{25}=\frac{xy}{25}$

Then area decreased %=$\frac{\frac{XY}{25}\times 100}{XY}=4$ %