Ratio

The ratio of two quantities a and b is the fraction a/ b and is expressed as a : b. Here a is the first term or antecedent and b is the second term or consequent. Since the ratio expresses the number of times one quantity contains the other, it is an abstract (without units) quantity.

A ratio remains unaltered if its numerator and denominator are multiplied or divided by the same number. eg, 4 : 3 is the same as (4 × 10) : (3 × 10) ie, 40 : 30.

“A ratio is said to be a ratio of greater or less inequality or of equality according as antecedent is
greater than, less than or equal to consequent”.
• If a > b, then a : b is called a ratio of greater inequality (eg, 4 : 3, 5 : 2, 11 : 3, ...)
• If a < b, then a : b is called a ratio of less inequality (eg, 3 : 4, 2 : 5, 3 : 11, ...)
• If a = b, then a : b is called a ratio of equality (eg, 1 : 1, 3 : 3, 5 : 5, ...)

From this we find that

• If a > b and some positive number is added to each term of a : b, then the ratio is diminished. If a > b, then (a + x) : (b + x) < a: b.
• If a < b and some positive number is added to each term of a : b, then the ratio is increased. If a < b, then (a + x) : (b + x) < a : b.
• If a = b and some positive number is added to each term of a : b, then the ratio is unaltered. If a = b, then (a + x) : (b + x) = a : b The price at which an article is sold is called the selling price or SP.

Kinds of Ratios

• Duplicate Ratio : a² : b² is called duplicate ratio of a : b.
• Triplicate Ratio : a³ : b³ is called triplicate ratio of a : b
• Sub-Duplicate Ratio
• Sub-triplicate Ratio
• Compound Ratio :  ab : cd is the compound ratio of a : c and b : d. It is the ratio of the product of the antecedents to that of the consequents of two or more given ratios.
• Inverse Ratio
• Componend and Dividend