Question : If the length of a rectangular plot of land is increased by 5% and the breadth is decreased by 10%, how much will its area increase or decrease?
Option 1: 6.5% increase
Option 2: 5.5% decrease
Option 3: 5.5% increase
Option 4: 6.5% decrease
Correct Answer: 5.5% decrease
Solution : Let $l$ be the length and $b$ be the breadth of the rectangle. Area of a rectangle = Length $\times$ Breadth Old area $=lb$ Length is increased by 5%. $\therefore$ New length $=l+\frac{5}{100}l = 1.05l$ Also, Breadth is decreased by 10%. $\therefore$ New breadth = $b-\frac{10}{100}b=0.9b$ $\therefore$ New area = $1.05l\times 0.9b = 0.945lb$ $\therefore$ Decrease in area = $\frac{\text{old area – new area}}{\text{old area}}\times 100$ = $\frac{lb-0.945lb}{lb}\times 100$ = 5.5% Hence, the correct answer is a 5.5% decrease.
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