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Arithmetic I

Ratio & Partnership

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CAT 2025 Lesson : Ratio & Partnership - Basics of Ratio & Shortcuts

The concepts of ratios can be used in any math question. Furthermore, ratio based questions or cases appear in Data Interpretation frequently. Therefore, it is imperative for you to have a strong understanding of the concepts covered in this lesson. This lesson will cover the basics of ratios, it's properties and concepts, and Partnership.

1. Ratios

Ratio is the quantitative relationship or comparison of numbers. It indicates the relationship of one quantity with respect to another.

For instance, if there are

8

chocolates and

12

toffees in a bag, then the ratio of chocolates to toffees in the bag is

8 : 12

, i.e.,

2 : 3

. The ratio indicates that for every

2

chocolates in the bag, there are

3

toffees.

A ratio can have 2 or more elements. For instance, if there are

20

Sri Lankans,

30

Indians and

40

Americans attending a conference, then the ratio of number of Sri Lankans, Indians and Americans at the conference will be

2 : 3 : 4

. So, for every

2

Sri Lankans at the conference, there are

3

Indians and

4

Americans.

A ratio of

2

numbers can be expressed as a fraction in this way ⇒

a : b = \dfrac{a}{b}

,

where a is called the antecedent and b is called the consequent

Like fractions, ratios can also be simplified and expressed.
Eg: Ratio of

8 : 32 = 1 : 4

Example 1

The ratio of girls to boys in a class was

2 : 1

. If there were

32

boys, how many girls were there in the class?

Solution

Let the number of girls in the class

= x

∴

\dfrac{\text{Girls}}{\text{Boys}} = \dfrac{2}{1} = \dfrac{x}{32}

⇒

x = 64

Answer:

64

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