Important concepts and formula to remember — lesson. Mathematics CBSE, Class 8.

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Basic Concepts:

To express \(x\) as a percentage of \(y\); percentage \(=\)

[\frac{x}{y} \times 100] %

If \(x\)\(\%\) of a quantity is \(y\), then the whole quantity \(=\)

[\frac{y}{x} \times 100] %

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 \(+\)

\frac{R}{100}

of Original quantity

\(=\)

[1 + \frac{R}{100}]

Original quantity

New quantity \(=\)

[\frac{100 + R}{100}] \times Original quantity

(II) Similarly, if quantity decreases by \(R\ \)\(\%\), then New quantity \(=\)

[\frac{100 - R}{100}] \times Original quantity

2. Population:

(I) If a population of a city increases by \(R\ \)\(\%\) per annum, then the population after '\(n\)' years \(=\)

{(1 + \frac{R}{100})}^{n}

of the original population.

Population after '\(n\)' years \(=\)

{(1 + \frac{R}{100})}^{n} \times Original population

(II) Population '\(n\)' years ago \(=\)

\frac{Original population}{{(1 + \frac{R}{100})}^{n}}

3. Rate is more/less than another:

(I) If a number \(x\) is \(R\)\(\%\) more than \(y\), then \(y\) is less than \(x\) by

(\frac{R}{100 + R} \times 100) %

(II) If a number \(x\) is \(R\)\(\%\) less than \(y\), then \(y\) is more than \(x\) by

(\frac{R}{100 - R} \times 100) %

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.

[\frac{x}{y} \times 100] %

(II) If the price of a commodity decreases by \(R\%\), then increases in consumption, so as not to increase the expenditure.

[\frac{y}{x} \times 100] %

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 \(=\)

\frac{R}{100}

Note: For increasing use (\(+\))ve sign and for decreasing use (\(-\))ve sign.

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2. Important concepts and formula to remember

Theory: