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
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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