Question
On increasing the length of a rectangle by 20% and decreasing its breadth by 20%, what is the change in its area?
- 20% increase
- 20% decrease
- No change
- 4% dcrease.
✓
Answer
- 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 $=\bigg[\bigg(\frac{\frac{1}{25}\text{xy}}{\text{xy}}\bigg)\times100\bigg]\%=4\%$
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