 ## Ratio | What is ratio?

A ratio is a comparison between two quantities of same kind or same unit in terms of fraction that shows how many times a quantity is of another quantity.

The ratio of two numbers ‘a’ and ‘b’ is written as a/b or a:b and is read as ‘a’ is to ‘b’. Similarly, ratio of ‘b’ and ‘a’ is written as b/a or b:a. Usually, the ratio of two quantities is written in the lowest term.

For example: Ratio between 40 kg and 70 kg is calculated by dividing 40 kg and 70 kg. Thus, the ratio = 40 kg/70 kg = 4/7 = 4:7. A ratio is a unit less term.

In the ratio a/b, a is called the first term (antecedent) and b is called the second term (consequent).

### Workout Examples

Example 1: Find the ratio of:
a.    80 cm to 2 m
b.    400 gm to 5 kg
c.     40 seconds to 4 minutes

Solution: Here,

Example 2: Two numbers are in the ratio of 3:5. If their sum is 48, find the numbers.

Solution: Here,
Ratio of two numbers = 3:5
Let, the numbers be 3x and 5x
3x + 5x = 48
or,        8x = 48
or,        x = 48/8
or,        x = 6
The numbers are: 3x = 3 × 6 = 18
5x = 5 × 6 = 30

Example 3: Two numbers are in the ratio of 3:4. If 4 is added to each number, the ratio becomes 11:14, find the numbers

Solution: Here,
Ratio of two numbers = 3:4
Let, the numbers be 3x and 4x
According to question,
(3x + 4)/(4x + 4) = 11/14
or,        11(4x + 4) = 14(3x + 4)
or,        44x + 44 = 42x +56
or,        44x – 42x = 56 – 44
or,        2x = 12
or,        x = 12/2
or,        x = 6
The numbers are: 3x = 3 × 6 = 18
5x = 4 × 6 = 24

You can comment your questions or problems regarding the ratio here.