Ratio and Proportion (TRICKS!!!)

(Article via. http://www.mastguru.com/)

1. What is Ratio

The ratio of two quantities a and b in the same units, is the fraction

ab

and we write it as a : b.

In the ratio a : b, we call a as the first term which is also know as antecedent and b, the second term which is also called consequent.

For example:

4:5=45

Here 4 is antecedent and 5 is consequent

Important Rule : 
The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

For example: 2:3 = 4:6 = 6:9

2. What is Proprotion

Equality of two ratios is called proportion. 

The equality of two ratios is called proportion.

If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.

Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.
Thus, a : b :: c : d <=> (b x c) = (a x d).

3. Fourth, third and mean proportional

i). Fourth Proportional:

If a : b = c : d, then d is called the fourth proportional to a, b, c.

ii). Third Proportional:

a : b = c : d, then c is called the third proportion to a and b.

iii). Mean Proportional:

Mean proportional between a and b is

ab−−√

4. Comparison of Ratios and Compounded Ratio

i). Comparison of Ratios: 
When we say that a:b > c:d, then it means

ab>cd

ii). Compounded Ratio:
The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf) 

Please note it is ratio of first ratio term of every ratio and second ratio term of every ratio

5. Important results of Ratio

i). Duplicate ratio of (a:b) is

(a2:b2)

ii). Sub-duplicate ratio of (a : b) is 

(a√:b√)

iii). Triplicate ratio of (a : b) is 

(a3:b3)

iv). Sub Triplicate ratio of (a : b) is 

(a13:b13)

v). 

ifthena+ba−b=c+dc−dab=cd,

6. Ratio Variation

i). We say that x is directly proportional to y, if x = ky for some constant k and we write, 

x∝y

ii). We say that x is inversely proportional to y, if xy = k for some constant k and
we write

x∝1y