# Ratio, Proportion and Variation

Ratio is a quantity which expresses the relationship between two similar quantities. It expresses a magnitude by which one quantity is a part of or a multiple of another quantity.

If the value of A and B are 8 and 6 respectively, then they are in the ratio 8:6 (read as 8 is to 6). Ratio can be understood also as the relationship which one quantity bears with the other of the same kind. Due to this reason, we cannot compare salary of one person with the percentage expenditure of another person.

The ratio of two quantities A and B is written as A:B. Here, A is known as an antecedent and B is known as a consequent. It can also be said that A:B = kA:kB, where k is any constant known as constant of proportionality, k â‰ 0.

If the antecedent is more than the consequent (or, the numerator is more than the denominator), then the ratio is known as an improper ratio.
For example, 5/3, 55/29, etc.

If the antecedent is more than the consequent (or, the numerator is more than the denominator), then the ratio is known as an improper ratio.

If the antecedent is less than the consequent (or, the numerator is less than the denominator), then the ratio is known as a proper ratio.
For example, 3/7, 7/18, etc.

Since Ratio compares two similar quantities, it cannot have any units.

Example-1

Consider any ratio . Now

*x*is added to the numerator and the denominator of this fraction. Which of the following is greater:Solution

It depends upon two factors:

- If the ratio is proper or improper
*x*is positive or negative.

If > 1 and

*x*> 0, or, < 1 and*x*< 0and if > 1 and

*x*< 0, or, < 1 and*x*> 0