Ratio and proportion Formula PDF: The ratio and proportion formula are explained in this article as the ratio and proportion formula play an important role in the Quantitative Aptitude section of the various competitive examinations. Candidates who are starting their preparation for the Government exams should learn the basic concepts of ratio and proportion during the starting stage of the preparation itself. After getting strong on the basic concepts of ratio and proportion, the candidates should practice the ratio and proportion formula for higher level questions for the main examination. In order to practice well on this topic the candidates should solve more questions on how to calculate ratio and proportion. Ratio and proportion is one of the most important topics in the prelims and mains examination of the banking exams. At least two questions will be asked in the ratio and proportion formula based problems. So practice well for the examination by solving high level questions in ratio and proportion formula.

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## Ratio and Proportion Formula PDF For Bank Exams

We have uploaded the ratio and proportion formula pdf for bank exams in this formula of ratio and proportion pdf for bank exams article. This ratio and proportion formula pdf will help you to solve the ratio and proportion questions easily by using the formula of ratio and proportion and it will save you time on the bank exams to concentrate on other questions. Ratio and proportion formula pdf will improve your speed and accuracy while solving the ratio and proportion questions by using the formula of ratio and proportion in the bank exams and other competitive exams.

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## Definition of Ratio

The definition of ratio is added in this formula of ratio and proportion for bank exams article. Ratio can be defined by the relationship between the two quantities which is obtained by dividing the first quantity by another. We can say that the two quantities a and b as a : b, such that b is not equal to 0. The numbers in ratio are compared only when they have the same units. The ratio is denoted by the symbol ‘ : ‘. For example, the formula of ratio can be expressed by a : b, a / b, a to b. This formula of ratio will be useful for various aptitude questions like partnership, ages, and more. So you must be familiar with the formula of ratio for your exams. You can also get the ratio and proportion formula by downloading the ratio and proportion formula pdf which will be very useful in the future.

## Definition of Proportion

The definition of proportion is added in this ratio and proportion formula for the bank exams article. Proportion can be defined as the given two ratios are equivalent to each other. When the given two sets of numbers are increasing or decreasing in the same ratio, then the ratios can be directly proportional to each other. There are three types of proportions. We have given a detailed explanation of the types of proportions in this formula of ratio and proportion article. We also added the types of proportions in the ratio and proportion formula pdf for the bank exams post. The types of proportions are,

• Direct Proportion
• Inverse Proportion
• Continued Proportion

## Formula of Ratio and Proportion

We have provided the various formula of ratio and proportion for bank exams here. The candidates who want to achieve more marks in the quantitative aptitude section of the bank exams shall go through this formula of ratio and proportion for bank exams post thoroughly. You can also download the ratio and proportion formula pdf for bank exams to be an expert with the formula of ratio and proportion for bank exams. It will make your calculations simpler and improve your speed and accuracy while solving the ratio and proportion questions by using the ratio and proportion formula for bank exams.

### Formula of Ratio:

We have added the formula of ratio in this formula of ratio and proportion for bank exams post. Here you can get to know the formula of ratio which is given below.

• If we have two quantities or two numbers and we have to find the ratio of these two, then the formula of ratio can be described as:

a: b ⇒ a/b

where a and b could be any two quantities.

Here, “a” is called the first term or antecedent, and “b” is called the second term or consequent. This is the important formula of ratio which will be very useful for your competitive exams.

For example, In ratio 3 : 8, is represented by 4 / 8,  where 3 is antecedent and 8 is consequent.

If we multiply and divide each term of the ratio by the same number (non-zero), it doesn’t affect the ratio.

Example: 3:8 = 6:16 = 9:24

### Formula of Proportion

We have added the formula of proportion in this formula of ratio and proportion for bank exams post. Here you can get to know the formula of proportion which is given below.

• Assume that, in proportion, the two ratios are a:b & c:d. The two terms ‘b’ and ‘c’ are called ‘mean terms,’ whereas the terms ‘a’ and ‘d’ are known as ‘extreme terms.’

a/b = c/d or  a : b :: c : d

For Example: Let us consider the number of students in a classroom. Our first ratio of the number of girls to boys is 4:6 and that of the other is 5:9, then the proportion can be represented as:

4: 6 ::  5: 9 or 4/6 = 5/9

Here, 4 & 9 are the extreme term, while 6 & 5 are the mean term.

### Fourth Proportion

• a: b ∷ c: x

x → Fourth Proportion

x=(b×c)/a

### Third Proportion

• a: b ∷ b: x

x → Third Proportion

Third Proportion of a, b = b²/a

### Mean Proportion

• a : x ∷ x : b

x → Mean Proportion

The mean proportion of ab is given by = √ab

• When two numbers are in the ratio a: b and their sum is x, then these numbers will be

ax/(a+b)  &  bx/(a+b)

• If three numbers are in the ratio of a : b : c and their sum is x then the numbers are

ax/(a+b+c) ,   bx/(a+b+c)  &  cx/(a+b+c)

• If a : b = n₁ : d₁ & b : c = n₂ : d₂

then a : b : c = n₁ × n₂ : n₂ × d₁ : d₁ × d₂

• If a : b = n₁ : d₁ , b : c = n₂ : d₂ , c : d = n₃ : d₃

a : b : c : d = n₁ × n₂ × n₃ : d₁ × n₂ × n₃ : d₁ × d₂ × n₃ : d₁ × d₂ × d₃

• If the ratio between two numbers is a: b & x is added to both of them then the ratio becomes c : d. Then the two numbers are given by:

• If the ratio of two numbers is a: b, then the number that should be added to each number to make the ratio c : d is given by

• The incomes of two persons are in the ratio → a: b and their expenditures are in the ratio → c : d. If the saving of each person is S, then their incomes are.

And their expenditures are given by

• When two ingredients A & B of quantities q₁ & q₂ with cost price/unit c₁ & c₂ respectively are mixed to get a mixture c having cost price cm/unit then.

(a) Ratio in which A & B are mixed

(q₁)/q₂ =(c₂-cm)/(cm-c₁ )

(b) Cost of the mixture

cm = (c₁×q₁+c₂×q₂)/(q₁+q₂)

## Difference Between The Ratio and Proportion

The difference between the ratio and proportion is provided in this formula of ratio and proportion for bank exams article and also in ratio and proportion formula pdf. Candidates shall take note of this ratio and proportion for bank exams article or download the formula of ratio and proportion pdf for bank exams for future reference.

 Difference Between The Ratio and Proportion Ratio Proportion It is used to compare the size of two quantities with the same unit. It is used to express the relation of two ratios It is expressed using a colon (:), slash (/) It is expressed using the double colon (::) or equal to the symbol (=) It is an expression It is an equation Example: a : b ⇒ a / b Example:a : b :: c: d⇒ a / b = c / s

Practice ratio and proportion questions - Free pdf

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## Formula of Ratio and Proportion With Examples

Example 1: There are 20 girls and 25 boys in a class. Find the ratio of the no. of boys to the total no. of students.

Solution

The ratio of the number of boys to the total no. of students by using the formula of ratio and proportion,

25/55= 5/11 = 5:11

Example 2: The weight of 72 boxes is 9 kg. What is the weight of 40 such boxes?

Solution

Weight of 72 boxes = 9 kg

Weight of 1 box = 9/72 kg = 1/8

So, weight of 40 boxes = 1/8*40 = 5 kg

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## Formula Ratio and Proportion For Bank Exams FAQs

Q. What is the formula of ratio?

A. If we have two quantities or two numbers and we have to find the ratio of these two, then the formula of ratio can be described as a: b ⇒ a/b

Q. What is the formula of proportion?

A. Assume that, in proportion, the two ratios are a : b & c : d. The two terms ‘b’ and ‘c’ are called ‘mean terms,’ whereas the terms ‘a’ and ‘d’ are known as ‘extreme terms.’

a/b = c/d or  a : b :: c : d

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