A quantity is increased by 12.5% and then decreased by 8.4%. Find the net percentage change.
3.05%
For successive percentage changes of \(x\%\) and \(y\%\), the net change is \(x + y + \frac{xy}{100}\).
Here, \(x = 12.5\) and \(y = -8.4\).
Substituting gives \(12.5 + (-8.4) + \frac{12.5 \times (-8.4)}{100} = 4.1 - 1.05\).
This gives a net change of \(3.05\%\).
Hence, the net percentage change is 3.05%.
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