Tips & Tricks: Ratio & Proportion

# Ratio and Proportion Tips and Tricks for Government Exams

## Introduction

• Ratio is a comparison of two quantities by division. Ratio represents the relation that one quantity bears to the other. It is represented as a:b. In any ratio a:b, a is called Antecedent and B is called Consequent. It is an abstract (without units) quantity.
A ratio remains unaltered if its numerator and denominator are multiplied or divided by the same number, e.g. 4:3 is the same as the (4 x 10) : (3 x 10) ie 40:30.
• Proportion is a statement that two ratios are similar. When two ratios are equal, they make a proportion, i.e. if a/b = c/d, then a, b, c and d are in proportion. This is represented as a:b :: c:d. When a, b, c and d are in proportion, then a and d are called the Extremes and b and c are called the Means, also Product of the Means = Product of the Extremes i.e. bc = ad.

### Theory

Ratio is a quantity which represents the relationship between two similar quantities. It expresses a magnitude by which quantity is multiple of another one. Ratio is represented as 2:3 or 2/3.
Here, numerator i.e. 2 is known as "ANTECEDENT" and denominator i.e. 3 is known as "CONSEQUENT".
If antecedent is more than the consequent, then it is known as improper ratio and if less ,then it is known as proper ratio.

### Different Types of Ratios

• Duplicate Ratio: a2 : b2 is called duplicate ratio of a : b.
• Triplicate Ratio: a3 : b3 is called triplicate ratio of a : b.
• Sub – Duplicate Ratio: √a :√b is called sub-duplicate ratio of a : b.
• Sub – Triplicate Ratio:∛a : ∛b is called sub-triplicate ratio of a : b Compound Ratio: ab : cd is the compound ratio of a : c and b : d. It is the ratio of the product of the antecedents to that of the consequents of two or more given ratios. Inverse Ratio: 1/a : 1/b is the inverse ratio of a : b.
• Componendo and Dividendo: If a/b = c/d, then (a + b)/(a – b) = (c + d)/(c – d)

### Different Types of Proportion

Continued Proportion: If these quantities a, b and c are such that a:b :: b:c, then b2 = ac and a, b and c are in continued proportion. Also the quantity c is called the third proportion of a and b.
Fourth Proportion: If four quantities a, b, c and x are such that a:b :: c:x, then ax = bc and x is called the fourth proportion of a, b and c.
Mean or second Proportion: If three quantities a, b and x are such that a:x :: x:b, then x2 = ab and x is called the mean of a and b. Also, if a:b = c:d, then the following properties holds good.

• b:a = d:c (Invertendo)
• a:c = b:d (Alternendo)
• (a + b) : b = (c + d) : d (Componendo)
• (a – b) : b = (c – d) : d (Divendendo)
• (a + b)/(a – b) = (c + d)/(c – d) (Componendo – Divendendo)

### Solved Examples

Question for Tips & Tricks: Ratio & Proportion
Try yourself:If x:y = 4:7, the  value of (x + y) /(x – y) = ?

Question for Tips & Tricks: Ratio & Proportion
Try yourself:Two numbers are in the ratio of 5:8. If 4 is subtracted from each then the ratio become 1:2. The small number is

Question for Tips & Tricks: Ratio & Proportion
Try yourself:x:y = 7:4 then (4x+7y) : (7x+4y)

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## Tips & Tricks for Government Exams

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## FAQs on Ratio and Proportion Tips and Tricks for Government Exams

 1. What is the difference between ratio and proportion?
Ans. Ratio is a comparison of two or more quantities, while proportion is an equation that states two ratios are equal.
 2. How do you simplify a ratio?
Ans. To simplify a ratio, divide both sides of the ratio by their greatest common divisor (GCD). This will give the simplest form of the ratio.
 3. What is the concept of direct proportion?
Ans. In direct proportion, as one quantity increases or decreases, the other quantity also increases or decreases by the same factor. This can be represented by an equation in the form of y = kx, where k is the constant of proportionality.
 4. How can I solve problems involving ratios and proportions?
Ans. To solve problems involving ratios and proportions, you can use cross multiplication or the unitary method. Cross multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio and vice versa. The unitary method involves finding the value of one unit and then using it to find the value of the required quantity.
 5. What are some real-life applications of ratio and proportion?
Ans. Ratio and proportion are used in various real-life situations such as cooking recipes, financial calculations, map scales, and mixing solutions. They are also used in engineering, architecture, and design to maintain the correct proportions of structures and objects.

## Tips & Tricks for Government Exams

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