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

$=$

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

$x$

$\%$ 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: