Question : The percentage change in a number when it is first decreased by 10% and then increased by 10% is:
Option 1: 0.1% increase
Option 2: 1% decrease
Option 3: 0.1% decrease
Option 4: No changes
Correct Answer: 1% decrease
Solution :
For successive percentage change use the following formula,
Net percentage change = ($x+y+\frac{xy}{100}$)%, where $x$ and $y$ are percentage increases or decreases, if increases take positive and if decreases take negative.
So, net percentage change = $- 10 + 10 + \frac{(-10) × (10)}{100}$
= $- 10 + 10 - 1$
= $- 1$%
[negative sign implies a decrease in percentage]
Hence, the correct answer is 1% decrease.
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