Question : The length and breadth of a rectangle are increased by 8% and 5%, respectively. By how much percentage will the area of the rectangle increase?
Option 1: 13.4%
Option 2: 15.4%
Option 3: 12.4%
Option 4: 16.4%
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Correct Answer: 13.4%
Solution :
Let the length and breadth be $l$ and $b$, respectively.
$\therefore$ Original area = $lb$
Length after 8% increase = $1.08l$
Breadth after 5% increase = $1.05b$
$\therefore$ New area = $1.08l\times 1.05b = 1.134lb$
$\therefore$ Percentage increase in area = $\frac{1.134lb-lb}{lb}\times 100$ = 13.4%
Hence, the correct answer is 13.4%.
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