Let’s focus on the subject of ratios and proportions

Posted: Date Posted – 11:25 PM Wed – 27 Jul 22

Hyderabad: In this series of articles, we will see how to solve the ratio and proportion questions, which is one of the essential topics for state government recruitment tests.

RATIO: The comparison between two quantities in terms of magnitude is called the ratio.

• It tells us that one quantity is how many times the other quantity.

• The relationship between a and b can be represented by a: b, where a is called antecedent and b is called consequent.

NOTE: 1. We are not comparing 10 boys and 8 cows, but we can compare the number (10) of boys and the number (8) of cows. Similarly, one cannot compare the number (20) of liters and the number (12) of toys etc.

2. The ratio has no units.


1. Duplication ratio: If a and b are two numbers, then the duplication ratio of a and b is a²:b².

Example: Duplicate ratio of 2:3 = 2²:3² = 4:9

2. Sub-duplication ratio: if a and b are two numbers, then the sub-duplication ratio of a and b is

Example: sub-duplication ratio of 16:25 = 4:5

3. Triple ratio: If a and b are two numbers, then the triple ratio of a and b is a³ : b³

Example: triple ratio of 7:9 = 7³:9³ = 343:729

4. Subtriple ratio: If a and b are two numbers, then the subtriple ratio of a and b is

Example: sub-triple ratio of 64:125 = 4:5

5. Inverse ratio: If a and b are two numbers, then the inverse ratio of a: b = b: a

Example: Inverse ratio of 2:3 = 3:2

6. Compound Ratio: If two or more ratios are given, the antecedent of one is multiplied by the antecedent of the other and the respective consequences are also multiplied. If a:b, c:d and e:f are three ratios, then their composite ratio will be ace:bdf

Example: The ratio composed of 2:3, 4:5 and 6:7

= 2 × 4 × 6: 3 × 5 × 7 = 48: 105


An equality of two ratios is called a proportion. We say that four numbers are proportional if or a : b = c : d then we say that a, b, c and d are proportional and can be written a : b : : c : d, where : : indicates the proportion ,

a and d are called extremes

b and c are called means

Example: 1:2::5:10

To be continued

Mr Venkat


MVK Publications



Jessica C. Bell