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**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).

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*Workout
Examples*

*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.*

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