MCQ
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
- CNo change
- ✓$4\%$ dcrease.
✓
Answer
Correct option: D.
$4\%$ dcrease.
Let :
Length $= x$
breadth $= y$
Area $ = xy$
Now,
New length $= x + 20\%\ x =\text{x}+\frac{1}{5}\text{x}=\frac{6}{5}\text{x}$
New breadth $= y - 20\%\ y =\text{y}-\frac{1}{5}\text{y}=\frac{4}{5}\text{y}$
New area $=\frac{6}{5}\text{x}\times\frac{4}{5}\text{y}=\frac{24}{25}\text{xy}$
Difference in the areas $=\text{xy}-\frac{24}{25}\text{xy}=\frac{1}{25}\text{xy}$
Difference in percentage $=\bigg[\bigg(\frac{\frac{1}{25}\text{xy}}{\text{xy}}\bigg)\times100\bigg]\%=4\%$
Length $= x$
breadth $= y$
Area $ = xy$
Now,
New length $= x + 20\%\ x =\text{x}+\frac{1}{5}\text{x}=\frac{6}{5}\text{x}$
New breadth $= y - 20\%\ y =\text{y}-\frac{1}{5}\text{y}=\frac{4}{5}\text{y}$
New area $=\frac{6}{5}\text{x}\times\frac{4}{5}\text{y}=\frac{24}{25}\text{xy}$
Difference in the areas $=\text{xy}-\frac{24}{25}\text{xy}=\frac{1}{25}\text{xy}$
Difference in percentage $=\bigg[\bigg(\frac{\frac{1}{25}\text{xy}}{\text{xy}}\bigg)\times100\bigg]\%=4\%$
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