Question : If the length of a rectangle is decreased by 13% and the breadth is increased by 13%, find the change of percentage in its area.
Option 1: 1.69% decrease
Option 2: 1.69% increase
Option 3: No change
Option 4: 13% decrease
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Correct Answer: 1.69% decrease
Solution : Given, The length of a rectangle is decreased by 13% and the breadth is increased by 13% We know, For successive, increase or decrease = $x + y + \frac{xy}{100}$ Here $x$ = 13 and $y$ = –13 ⇒ $13 + (-13) + \frac{(13)(-13)}{100}=-\frac{169}{100}=-1.69$% So a 1.69% decrease. Hence, the correct answer is '1.69% decrease'.
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