An equation where two ratios are said to be equivalent is known as proportion. Suppose p, q, r and s are said to be in proportion , then

The proportion formula is,

p : q :: r : s $\Rightarrow$ $\frac{p}{q}$ = $\frac{r}{s}$.
Where,
p & s are extremes,
q & r are mean terms.

If the cross products of the two ratios are equal then the ratios are equivalent.

Proportion Solved Examples

Based on proportion, below are some of the examples given:

Question 1: Find the value of x in the following equation:
5 : 10 :: x : 2.
Solution:
Given: 5 : 10 :: x : 2

$\Rightarrow$ $\frac{5}{10}$ = $\frac{x}{2}$

x = $\frac{5}{10}$ $\times$ 2

x = $\frac{5}{5}$

x = 1

Therefore, 5 : 10 :: 1 : 2.

Question 2: Find the value of x in the following equation:
3 : x :: 6 : 12.
Solution:
Given: 3 : x :: 6 : 12

$\Rightarrow$ $\frac{3}{x}$ = $\frac{6}{12}$

x = $\frac{3 \times 12}{6}$

x = $\frac{36}{6}$

x = 6

Therefore, 3 : 6 :: 6 : 12.