Percentage Change Calculation for Income Fluctuations
This question asks us to find the net effect on a person's income after it's first increased by 10% and then subsequently decreased by 10%. We need to determine the overall percentage change in the income.
Method 1: Using an Assumed Initial Income
Let's assume the person's initial income was a convenient amount, say $ \text{₹}100 $. We can track the changes step-by-step:
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Calculate the income after the 10% increase:
- Increase Amount = $ 10\% $ of $ \text{₹}100 $
- $ \text{Increase Amount} = \frac{10}{100} \times 100 = \text{₹}10 $
- Income after increase = Initial Income + Increase Amount
- $ \text{Income after increase} = \text{₹}100 + \text{₹}10 = \text{₹}110 $
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Calculate the income after the 10% decrease:
The decrease is calculated on the new income ( $ \text{₹}110 $).
- Decrease Amount = $ 10\% $ of $ \text{₹}110 $
- $ \text{Decrease Amount} = \frac{10}{100} \times 110 = \text{₹}11 $
- Final Income = Income after increase - Decrease Amount
- $ \text{Final Income} = \text{₹}110 - \text{₹}11 = \text{₹}99 $
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Calculate the net change in income:
- Net Change = Final Income - Initial Income
- $ \text{Net Change} = \text{₹}99 - \text{₹}100 = -\text{₹}1 $
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Calculate the net percentage change:
- Percentage Change = $ \left( \frac{\text{Net Change}}{\text{Initial Income}} \right) \times 100\% $
- $ \text{Percentage Change} = \left( \frac{-1}{100} \right) \times 100\% = -1\% $
A negative percentage indicates a reduction. Therefore, the person's income is reduced by 1%.
Method 2: Using the Percentage Change Formula
A common scenario involves successive percentage changes. If a value is increased by $ x\% $ and then decreased by $ y\% $, the net percentage change is given by:
$ \text{Net Change \%} = \left( x - y - \frac{xy}{100} \right) \% $In this problem:
- The increase is $ x = 10\% $.
- The decrease is $ y = 10\% $.
Plugging these values into the formula:
$ \text{Net Change \%} = \left( 10 - 10 - \frac{10 \times 10}{100} \right) \% $ $ \text{Net Change \%} = \left( 0 - \frac{100}{100} \right) \% $ $ \text{Net Change \%} = (0 - 1) \% $ $ \text{Net Change \%} = -1\% $The result $ -1\% $ signifies a net decrease of 1% in the income.
Conclusion
Both methods show that after a 10% increase followed by a 10% decrease, the income ultimately reduces by 1%.
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?
