RATIO AND PROPORTION
RATIO: The number of times one quantity contains another quantity of the same kind. The comparison is made by considering what part or multiple the first quantity of the second.
Thus the ratio between 5 apples and 15 apples can be possible, but not between Rs 150 and 25 kgs of rice.
The ratio between one quantity to another is denoted by a : b or by a fraction 
Ex: 2:3 or 5:11 etc.
The two quantities in the ratio are called its terms.
The first term is called the antecedent and the second is called consequent.
The terms of the ratio can be multiplied or divided by the same number.
Types of Ratios:
- Duplicate ratio: The ratio of the squares of the two numbers.
Ex: 9 : 16 is the duplicate ratio of 3 : 4.
- Triplicate Ratio: The ratio of the cubes of the two numbers.
Ex: 125: 512 is the triplicate ratio of 5 : 8.
- Sub-duplicate Ratio: The ratio between the square roots of the two numbers.
Ex: 2 : 5 is the sub-duplicate ratio of 4 : 25.
- Sub-triplicate Ratio: The ratio between the cube roots of the two numbers.
Ex: 4 : 7 is the sub-triplicate ratio of 64 : 343.
- Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first.
Ex: 3 :5 is the inverse ratio of 5 : 3.
- Compound ratio: The ratio of the product of the first terms to that of the second terms of two or more ratios.
