Ratio

Ratio and Proportion
Ratio is a relationship between two numbers that indicates how many times the first number contains the second. Suppose I bought 2 orange and 8 apples then the ratio of oranges to apple is two to eight.

This ratio can be therefore written as 2: 8 which is equivalent to 1: 4.
A ratio is a comparison of two numbers. For example, if 25 students -- 10 boys and 15 girls -- are in your class, then the ratio of boys to girls is 10 to 15.
The numbers compared in ratio can be any quantities of a comparable kind such as lengths, persons, any objects etc. The ratio of numbers a and b can be expressed as
1. a to b
2. a is to b
3. a : b
In ratio the numbers a and b are called antecedent and consequent respectively.
Ratios are sometimes used with three or more terms. Have you ever gone to a construction sites? A mason mixes sand, cement and water in a proper ratio. If for every 2 kg of sand and 4 kg of cement the mason mixes 9 kg of water then the ratio in this circumstance is 2: 4: 9.

According to the Oxford English Dictionary online, ratio is 'the relation between two similar magnitudes in respect of quantity, determined by the number of times one contains the other (integrally or fractionally)'.
It means the ratio can be expressed in fraction. The ratio of oranges to that of apple as taken above can be written in fraction as 2/8.

There can be a ratio between `100 aand `500 but there can’t be the ratio between `500 and 1000 apples.
Types of Ratio

 Duplicate Ratio: - If two numbers are in ratio, then the ratio of their squares is called duplicate ratio. The duplicate ratio of two numbers a and b is a^2: b^2.
Example: - Duplicate ratio of 5: 6 is 5^2: 6^2 = 25: 36

 Sub- duplicate Ratio: - If two numbers are in ratio then the ratio of their square roots is called sub- duplicate ratio. The sub-duplicate ratio of a and b is a^1/2 : b^1/2
Example: - Sub duplicate of 25: 36 = √25: √36 = 5 : 6

 Triplicate ratio: - If two numbers are in ratio, then the ratio of their cubes is called triplicate ratio. The triplicate ratio of two numbers a and b is a^3: b^3.
Example: Triplicate ratio of 2: 5 is 2^3: 5^3 = 8: 125

 Sub- triplicate ratio:- If two numbers are in ratio, then the ratio of their cube- root is called sub-triplicate ratio. The sub-triplicate ratio of two numbers a and b is a^1/3: b^1/3.
Example:- Sub- triplicate ratio of 8 : 125 is 2: 3

 Inverse Ratio: - If two numbers are in ratio such that when the antecedent and consequent of ratio is interchanged a new ratio is obtained which is called Inverse ratio. The inverse ratio of a: b is b : a.
Example:- Inverse ratio of 4 : 7 is 7 : 4

 Compound Ratio:- If two or more ratio are given, then the antecedent of one is multiplied with antecedent of other and respective consequents are also multiplied then we get compound ratio. If a : b , c : d, e : f are three ratio then their compound ratio will be ace : bdf
Example: The compound ratio of 2 : 5 , 5 : 9 and 7 : 18 is 2 x 5 x 7 / 5 x 9 x 18 = 7 : 81


Dr Rajesh Kumar Thakur