Ratio and Proportion

Definition of Ratio:

Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part, or parts, one quantity is of the other.

The ratio of \( A \) to \( B \) is usually written \( A : B \). The quantities \( A \) and \( B \) are called the terms of the ratio. The first term is called the antecedent, the second term the consequent.

To find what multiple or part \( A \) is of \( B \), we divide \( A \) by \( B \), hence the ratio \( A : B \) may be measured by the fraction \( \frac{A}{B} \), and we shall usually find it convenient to adopt this notation.

In order to compare two quantities they must be expressed in terms of the same unit. Thus the ratio of Rs. 2 to 15 np. is measured by the fraction \( \frac{2 \times 100}{15} \) or \( \frac{40}{3} \).