# (Guidance Programme) Combined Higher Secondary Level [CHSL] (10+2) Exam : Ratio & Proportion

## (Guidance Programme) Combined Higher Secondary Level [CHSL] (10+2) Exam : Ratio & Proportion

## 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 : a
^{2}: b^{2}is called duplicate ratio of a : b. - Triplicate Ratio : a
^{3}: b^{3}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