Question : The length of a rectangle is increased by 10% and breadth is decreased by 10%. The area of the new rectangle is:
Option 1: neither increased nor decreased.
Option 2: increased by 1%.
Option 3: decreased by 2%.
Option 4: decreased by 1%.
Correct Answer: decreased by 1%.
Solution :
Let the length and breadth of the rectangle be $a$ and $b$ respectively.
Initial area = $ab$ sq. units
Length after 10% increase = $a + \frac{10}{100}\times a = 1.1a$
Breadth after 10% decrease = $b - \frac{10}{100}\times b = 0.9b$
$\therefore$ New area becomes = $1.1a \times 0.9b = 0.99ab$ sq. units
So, percentage decrease in area = $\frac{ab-0.99ab}{ab}\times$ 100 = 1%
Hence, the correct answer is decreased by 1%.
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