Ratio And Proportion

Video Lesson on Ratio And Proportion

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon ":". Suppose we want to write the ratio of 8 and 12.

We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.


  • The ratio of two quantities a and b of same units is the fraction x/y, where b ? 0
  • The fraction x/y can be represented as x:y

Different types of ratios are:

The concept of ratio & proportion is used in quantitative as well as DI section. Grocery shopping, selling, cooking to industries production- everything makes use of the concept of ratio, proportion & mixtures. Partnership assumes significance in the business world, where various business partners need to distribute profits according to their share of investments and time period. Here, you will learn the formulae & shortcuts to solve questions based on ratio, mixtures and partnership.

1) Duplicate ratio:

It is the ratio of squares of two numbers.

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2) Sub-duplicate ratio:

It is the ratio between square roots of two numbers.

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3) Triplicate ratio:

It is the ratio of cubes of two numbers.

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4) Sub- Triplicate ratio:

It is the ratio between cube roots of two numbers

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5) Compound ratio:

It is the ratio of product of first terms in every ratio to that of product of second term in every ratio.
For example: Compound ratio of (a : x), (b : y), (c : z) is (abc : xyz)

6) Inverse ratio:

The ratio formed by interchanging their old places in the ratio to new
The inverse ratio of 5 : 8 is 8 : 5.

Section MCQ Full Section (3 MCQ)
Topic Para Based MCQ
Topic Questions with Answers


  • 1) Proportion is the equality of two ratios.
    When (a : b = x : y) is represented as (a : b :: x : y), then a, b, x, y are said to be in proportion.
    In (a : b :: x : y), a and y are called as extremes and b and x are called as mean terms.
    Product of means = Product of extremes
  • 2) Mean proportion: Mean proportion between x and y is given as xy
  • 3) Third proportion: If p : q = q : s, then s is called as third proportional to p and q.
  • 4) Fourth proportion: If u : v = x : y, then y is the fourth proportional of u, v and x.

Quick Tips and Tricks

1) Comparison of ratios:

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2) Proportion

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4) Variation:

  • If a = kb for some constant k, then we can say that a is directly proportional to b.
  • If ba =k for some constant k, then we can say that a is inversely proportional to b.

5) Ratio between first and second quantity

If ratio between first and second quantity m : n = a : x, second and third quantity n : p = b : y, fourth and fifth quantity p : q = c : z, then m : n : p : q can be easily solved by using the trick shown below:
r7 -42380548 m : n : p : q = abc : xbc: xyc : xyz

6) If a number a is divided in the ratio x : y,

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