Let’s focus on ratio and proportion topic

In this series of articles, we will look into how to solve the questions on Ratio and Proportion, which is one of the essential topics for State government recruitment exams.

Ratio: The comparison between two quantities in terms of magnitude is called the ratio.
– It tells us that the one quantity is how many times the other quantity.
-The ratio between a and b can be represented as a : b, where a is called antecedent and b is called consequent.

Note:
• We do not compare 10 boys and 8 cows, but we can compare the number (10) of boys and number (8) of cows. Similarly, we cannot compare the number (20) of litres and the number (12) of toys etc.
• Ratio has no units.

Types of ratio:

1. Duplicate ratio: If a and b are two numbers, then the duplicate ratio of a and b is a² : b².
Example: Duplicate ratio of 2 : 3
= 2² : 3² = 4 : 9

2. Sub-duplicate ratio: If a and b are two numbers, then sub-duplicate ratio of a and b is √a : √b

Example: Sub-duplicate ratio of
16 : 25 = √16 : √25 = 4 : 5

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

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

4. Sub-triplicate ratio: If a and b are two numbers, then the sub-triplicate ratio of a and b is ∛a : ∛b

Example: Sub-triplicate ratio of ∛64 : ∛125 = 4 : 5

5. Inverse ratio: If a and b are two numbers, then the inverse ratio of a : b = 1/a : 1/b = b : a

Example: Inverse ratio of 2 : 3 = 1/2 : 1/3 = 3 : 2

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

Example: The compound ratio of 2 : 3, 4 : 5, and 6 : 7
= 2 × 4 × 6 : 3 × 5 × 7
= 48 : 105

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

Example: 1 : 2 :: 5 : 10
 

M Venkat
Director
MVK Publications
Dilsukhnagar
7671002120