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Basic Concepts:
To express \(x\) as a percentage of \(y\); percentage \(=\)
If \(x\)\(\%\) of a quantity is \(y\), then the whole quantity \(=\)
Fundamental Formulae:
1. Increase/Decrease in quantity:
(I) If quantity increases by \(R\)\(\%,\) then [Where \(R\) denotes the rate of change in percentage]
New quantity \(=\) Original quantity \(+\) Increases in the quantity
\(=\) Original quantity \(+\) \(R\)\(\%\) of Original quantity
\(=\) Original quantity \(+\) of Original quantity
\(=\) Original quantity
New quantity \(=\) .
(II) Similarly, if quantity decreases by \(R\ \)\(\%\), then New quantity \(=\)
2. Population:
(I) If a population of a city increases by \(R\ \)\(\%\) per annum, then the population after '\(n\)' years \(=\) of the original population.
Population after '\(n\)' years \(=\)
(II) Population '\(n\)' years ago \(=\)
3. Rate is more/less than another:
(I) If a number \(x\) is \(R\)\(\%\) more than \(y\), then \(y\) is less than \(x\) by
(II) If a number \(x\) is \(R\)\(\%\) less than \(y\), then \(y\) is more than \(x\) by
4. Prices of a commodity Increase/Decrease by R \(\%\):
(I) If the price of a commodity increase by \(R\%\), then a reduction in consumption, so as not to increase the expenditure.
(II) If the price of a commodity decreases by \(R\%\), then increases in consumption, so as not to increase the expenditure.
If a quantity is increased or decreases by \(x\%\) and another quantity is increased or decreased by \(y\%\), the percent \(\%\) change on the product of both the quantity is given by require \(\%\) change \(=\)
Note: For increasing use (\(+\))ve sign and for decreasing use (\(-\))ve sign.
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