Ratio:
A ratio is a comparison of the sizes of two or more quantities of the same kind by division. The comparison between two similar things, in the same unit, is based on the magnitude of the things.
If a and b are two quantities of the same kind, then the fraction a/b is called the ratio of a to b and is written as a: b. the quantities a and b are called the terms of the ratio,

is called the ist term or antecedent

b is called the 2nd term or consequent

Points to be remember while calculating ratio:
(a) A ratio is expressed in lowest terms. Both terms of a ratio can be multiplied or divided by the same (non-zero) number. For example,
15           :               20                                           = 3          :               4
↓                          ↓                                           (dividing both terms by 5)
Antecedent          Consequent

(b) Ratio exists only between quantities of the same kind. For example, there is no ratio between the weight of one child and the age of the another child.

(c) Quantities to be compared (by division) must be in the same units. For example, ratio between 25 minutes and 45 seconds          = ratio between (25*60) sec and 45 sec
= 1500/45 = 100/3 = 100: 3

(d) When a quantity is increased in a certain ratio multiply the quantity by the greater ratio. For example, production of fan which was 1000 in the last year has increased in the ratio of 5:7, then the new production will be =1000*(7/5) = 1400.

(e) When a quantity is decreased in a certain ratio, multiply the quantity by the lessor ratio. For example, production of fan which was 1000 in the last year has decreased in the ratio of 10:5, then the new production will be =1000*(5/10) = 500.

(f) When both increase and decrease of quantity are present in a problem, multiply the quantity by the greater ratio, in case of increase and then multiply the result by lessor ratio to obtain the final result. For example, production of fan which was 1000 in the last year, has increased in the ratio of 5:7 at first, but subsequently decreased in the ratio of 10 :5,then the new production will be =1000*(7/5)*(5/10) = 700.

Calculation of various kind of ratio:

Inverse Ratio: One ratio is the inverse of another if their product is 1. For example, inverse ratio of 3:5 is 5:3 since (3:5)*(5:3) = 1.

Compound Ratio: Compound ratio of 2:5 and 3:7 = (2*3): (5*7) = 6: 35.

Duplicate Ratio: A ratio compounded itself is called its duplicate ratio. For example,
Duplicate ratio of a: b is a2: b2
Triplicate ratio of a: b is a3: b3

Sub-duplicate ratio of a: b is √a: b
Sub-triplicate ratio of a: b is 3a: 3b