# Rapid Revision for CSIR NET Part A: Formula Sheets on Ratio And Proportion - Check Here!!!

By Astha Singh|Updated : February 7th, 2022

CSIR NET Part-A Formula Sheet: During the preparation, the candidates study different formulas to solve problems, but at the last moment, these formulas might not be remembered by the candidates due to exam fear or pressure. We at BYJU'S Exam Prep do not want our students to lag anywhere during the preparation, so we have come up with a concept of a Formula Sheet that will help them revise the important formulas at the last moment. This formula sheet will be a short revision tool and contain only important formulas that need to be studied at the last minute to boost the score. Our experienced subject-matter experts have meticulously designed this CSIR NET General Aptitude Formula Sheet to provide you with the best authentic material.

In this article, we will cover the CSIR NET General Aptitude Most Important Formulas of Ratio And Proportion. Aspiring candidates can check all the most important formulas of Ratio And Proportion for the last minute revision. Scroll down the full article to find out!

Ratio And Proportion

Definition of Ratio:

Comparison of two different quantities having the same units.

Types of Ratio:

Let us assume that, two numbers are ‘a’ and ‘b’.Then the ratio is a: b.

Therefore,

⦁ Duplicate ratio: a2: b2

⦁ Sub duplicate ratio:

⦁ Triplicate ratio: a3: b3

⦁ Sub triplicate ratio:

⦁ Inverse ratio:

⦁ If three different ratios are a: b, c : d and d: e

Compounded ratio:
Some important properties of ratio:

⦁ If in the ratio a/b, the numerator and the denominator are multiplied or divided by the same number then the value of the ratio remains the same.

Case 1: Multiplying numerator and denominator by same number x: Ratio = Thus, cancelling out x further results in the same ratio a/b.

Case 2: Dividing numerator and denominator by same number y: Ratio = Thus, cancelling out y further results in the same ratio a/b.

2. If p/q = r/s = t/u = v/w = m then m =
Comparison of two ratios: Suppose we have to compare two different ratios 12/17 and 13/11. Here to find which ratio is greater or lesser than the other, we use the cross multiplication method. Simply cross multiply the denominator to the numerator of another ratio.
(12×11) (13×17) = 132 221 Comparing we get 132 < 221 thus.

Proportion: If two ratios are equal then the 4 terms are called proportion. For example:  = It can also be written as: a : b:: c : d Here terms a and d are called extremes and terms c and d are called means.
Types of Proportion: If the ratio is a: b

⦁ Mean proportion:

⦁ Third proportion:

⦁ If three numbers a, b and c are given then

Fourth proportion:

Note:

⦁ If a: b = 2 : 3 and b: c = 4: 5 Then

⦁ If a : b = 1 : 2, b : c = 3 : 4 and c : d = 2 : 3

⇒ a : b : c : d = 6 : 12 : 16 : 24

Example 1: If 2a = 3b = 4c = 5d then find a : b : c : d.

Solution:
2a = 3b = 4c = 5d = (60) = LCM of (2,3,4,5)

⇒ a : b : c : d = 30 : 20 : 15 : 12

Example 2: If a : (b + c) = 1 : 2 and b : (c + a) = 3 : 4 then find c : (a + b).

Solution:
In first case: a + (b + c) = 1 + 2 = 3
In second case: b + (c + a) = 3 + 4 = 7
Now multiplying first equation with 7 and Second equation with 3: a : (b + c) = 7 : 14 and b : (c + a) = 9 : 12 Thus, by comparison:
a = 7 b = 9
So, c = 21 – (7 + 9) = 5
Thus, c : (a + b) = 5 : 16

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