Ratio and Proportion

Ratio: Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent.

Proportion: a, b, c and d are said to be proportion if a : b = c : d.
a and d are called the extremes, b and c are called the means. a, b, c and d are called first proportion, second proportion, third proportion and fourth proportion respectively.

Types Of Ratios and Proportion:

Ratios are classified in to six types:

1) Duplicate ratio:The ratio of the squares of the two numbers.Ex: 9:16 is the duplicate ratio of 3:4.

2) Triplicate ratio:The ratio of the cubes of the two numbers.Ex: 27:64 is the triplicate ratio of 3:4.

3) Sub-duplicate ratio:The ratio between square root of the two numbers.Ex: 4:5 is the sub-duplicate ratio of 16:25.

4) Sub-triplicate ratio:The ratio between the cube roots of the two numbers.Ex: 4:5 is the sub-triplicate of 64:125.

5) Inverse ratio:If the two terms in the ratio interchange their places,then the new ratio is inverse ratio of the first.Ex: 9:5 is the inverse ratio of 5:9.

6) Compound ratio:The ratio of the product of the first term to that of the second term of two or more ratios.Ex: 3/4,5/7,4/5 and 3/5 is 3/4 x 5/7 x 4/5 x 3/5 = 9/35.

Proportions are classified in to four types:

1) Continued proportion:In the proportion 8/12=12/18, 8,12,18 are in the continued proportion.

2) Fourth proportion:If a:b=c:x,then x is called forth proportion of a,b and c.The fourth proportion of a,b.c =bc/a

3) Third proportion:If a:b=b:x,then x is called third proportion of a and b.Third proportion of a,b =b^2/a

4) Second or mean proportion: If a:x=x:b,then x is called second or mean proportion of a and b.Therefore mean proportion of a and b =Root of(ab)