Question : A number is first increased by 10% and then increased by 20%. The number, so obtained, is now decreased by 12%. What is the net increase or decrease percent in the original number?
Option 1: 16.16% increase
Option 2: 14.14% decrease
Option 3: 11.11% decrease
Option 4: 12.12% increase
Correct Answer: 16.16% increase
Solution :
The formula for two successive percentage changes (increase or decrease) is given by:
$\text{Net percentage change} = a + b + \frac{ab}{100}$
where $a$ and $b$ are the two percentage changes.
In this case, the number is first increased by 10% and then by 20%, so $a = 10$ and $b = 20$. Substituting these values into the formula, we get:
$\text{Percentage increase} = 10 + 20 + \frac{10 \times 20}{100} = 32\%$
Then the number is decreased by 12%, so now $a = 32$ and $b = -12$. Substituting these values into the formula, we get:
$\text{Net change} = 32 - 12 + \frac{32 \times -12}{100} = 16.16\%$
So, there is a net increase of 16.16% in the original number.
Hence, the correct answer is a 16.16% increase.
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