Ratio and Proportion: Ratio and Proportion is one of the important scoring topics in the whole quantitative Aptitude. There are several examinations such as SSC CGL Tier 2, SSC CHSL, etc lined up in the upcoming months, candidates must have started preparing for the tougher sections thoroughly. The quantitative ability questions are asked in almost every government job examination with a special focus on ratio and proportion. Here we at re providing you with detailed knowledge regarding the Ration and Proportion starting from the definition, formulas, tips, and tricks for solving the questions.
Ratio and Proportion
Ratio and Proportion are the fractions. When the fraction is represented in the form of a:b, then it is a ratio and a proportion states that two ratios are equal. A and b are any two integers. Ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics.
What is Ratio?
The ratio can be defined as the relationship between two quantities such as a:b, where b is not equal to 0. The two numbers in a ratio can only be compared when they have the same unit. Ratios are used to compare two things. The ratio is denoted by the sign ‘:’. The ratio can be represented as follows.
- a to b
- a: b
For Example, The ratio of 4 to 8 is represented as 4:8 = 1:2. And the statement is said to be in proportion.
What is Proportion?
Proportion is an equation that defines that the two given ratios are equivalent to each other. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. There are 3 types of Proportion i.e.
- Direct Proportion
- Inverse Proportion
- Continued Proportion
Ratio and Proportion Formula
- Fourth Proportion
Example. Find the fourth proportion to the numbers 4, 10, and 12.
- Third Proportion→
Find the third proportion to the numbers 4, 12.
Ratio and Proportion Examples
- If two numbers are in the ratio a: b and their sum is x, then these numbers will be
- If three numbers are in the ratio of a : b : c and there sum is x then the numbers are
- If a : b = n₁ : d₁ & b : c = n₂ : d₂
- If a : b = n₁ : d₁ , b : c = n₂ : d₂ , c : d = n₃ : 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.
- 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.
Ratio and Proportion: FAQ
Q. What are Ratios and Proportions?
Ans: Ratio is the comparison between the quantities with the same unit. It is obtained by dividing the first quantity by the other.
Q. What is the Formula of Ratio and Proportion?
Ans: The ratio formula for any two quantities is expressed as a: b ⇒ a/b. On the other hand, the proportion formula is expressed as a:b::c:d⟶ab=cda:b::c:d⟶ab=cd.