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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.

  1. a to b
  2. a: b
  3. 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.

Overview: Ratio & Proportion | Quantitative Aptitude (Quant) - CAT

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.

  1. Direct Proportion
  2. Inverse Proportion
  3. Continued Proportion

Ratio and Proportion Formula

a: b ∷ c : d
Product of Means = Product of Extremes
a×d = b×c
  • Fourth Proportion
a: b ∷ c: x
x → Fourth Proportion
x=(b×c)/a

Examples

Example1: Find the fourth proportion to the numbers 4, 10, and 12.
Sol: Fourth Proportion
=(12×10)/4
= 30

  • Third Proportion→ 
a: b ∷ b: x
x → Third Proportion
Third Proportion of a, b = b²/a

Ratio and Proportion Examples

Example 1: Find the mean proportion of 4, 16?
Sol: Mean proportion = √(4×16)
=√64
= 8
  • If 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 there 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
Example2:  If A : B = 3 : 5 & B : C = 9 : 10, find A : B : C.
Sol. A : B = 3 : 5
B : C = 9 : 10
A : B : C = 3 × 9 : 9 × 5 : 5 × 10
= 27 : 45 : 50
  • 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
The document Overview: Ratio & Proportion | Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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FAQs on Overview: Ratio & Proportion - Quantitative Aptitude (Quant) - CAT

1. What is a ratio?
A ratio is a mathematical comparison between two or more quantities. It shows the relationship between the quantities in terms of their relative sizes or amounts.
2. How is a ratio expressed?
A ratio is expressed in the form of two numbers separated by a colon (e.g., 2:3) or as a fraction (e.g., 2/3). The numbers in the ratio represent the number of times one quantity is contained within the other.
3. What is a proportion?
A proportion is an equation that states two ratios are equal. It shows that two sets of quantities are in balance or have the same relationship. Proportions are often used to solve problems involving unknown quantities.
4. How do you solve a proportion?
To solve a proportion, you can use the cross-multiplication method. Multiply the numerator of the first ratio by the denominator of the second ratio, and then multiply the denominator of the first ratio by the numerator of the second ratio. Set these two products equal to each other and solve for the unknown quantity.
5. How are ratios and proportions used in real-life situations?
Ratios and proportions are used in various real-life situations such as cooking recipes, financial calculations, scale models, and map scaling. They help to compare quantities, find unknown values, and maintain balance in different contexts.
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