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.

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.