# Principle of Proportionality

**Introduction to principle of proportionality**

In mathematics, two quantities are said to be **proportional** if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.

The principle of Proportionality also refers to the equality of two ratios.

Proportionality is denoted by the symbol `oo`

Types of proportionality

Direct proportionality

Inverse proportionality

## Principle of Direct Proportionality

Let two variables x and y. If x varies directly proportional to y,

then those two variables can be expressed as, y `oo`

To remove the proportionality symbol, we introduce a constant "k" called as proportionality constant,

now the proportionality expression becomes, y = kx

**Example problem to explain the principle of direct proportionality**

If the value of y varies directly with the value of x and y = 8 when x = 2. Calculate the value of y when x = 12.

**Sol**

Given, y `oo`

So, y = kx

We know, y = 8 and x = 2. plug these values in the equation to find the value of k.

8 = 2k

k = 4

Now the equation becomes,

y = 4k

To find the value of y when x = 12,

plug k = 4 and x = 12 in y = kx

y = 4 * 12

**y = 48**

## Principle of Inverse Proportionality

If two variables are inversely proportional to each other, say x and y.

`y` `oo` `1/x`

By introducing a proportionality constant, k

`y` = `k/x`

**Example problem to explain the principle of inverse proportionality**

If the value of y varies inversely with the value of x and y = 8 when x = 2. Calculate the value of y when x = 12.

Sol

We know the equation for inverse proportionality, `y` = `k/x`

Plug x = 2 and y = 8 in the equation to find the value of k,

8 = `k/2`

k = 16

Now the equation becomes, y = `16/x`

Now we have to find the value of y when x = 12.

Plug x = 12 in the above equation

y = `16/12`

**y = `4/3`**