Here is a quick Guide for those who are preparing for bank or other exams for Ratio and Proportion Problems. You will get Shortcut Tricks & Tips with proper examples, Questions & Answers for MCQs i.e. Objective Questions. Also these Study Notes can be downloaded in PDF from the button provided above.
Contents
Ratio
Ratio is simple p/q form where p is numerator and q is denominator.It is represented by p:q.In hindi,numerator is called as “ansh (अंश)” and denominator is called as “har (हर)”.
Example: is a ratio where 4 is numerator and 5 is denominator.
Note: Multiplication and division of each term of a ratio by nonzero ratio will not affect on the ratio.
Example : 4 : 3 = 8 : 6 = 12 : 9 etc.
Types of ratio

Duplicate ratio
If ratio is a : b then duplicate ratio is : .
Example: Ratio is 4 : 5 then duplicate ratio is 16 : 25. 
Subduplicate ratio
If ratio is a : b then subduplicate ratio is : .
Example : Ratio is 25 : 36 then subduplicate is 5 : 6.

Triplicate ratio
If ratio is a : b then triplicate ratio is .
Example: Ratio is 5 : 6 then triplicate ratio is 125 : 216.

Subtriplicate ratio
If ratio is a : b then subtriplicate ratio is : .
Example: Ratio is 64 : 125 then subtriplicate is 4 : 5.

Comparison of ratio
If (a : b ) > (c : d ) .
Example: Which is greater ratio – and.
Answer is .

Compounded ratio
Ratios are (a : b),(c : d) ,(e : f) is (ace : bdf).
Example: The ratio is ( 5 : 6),(4 : 3) and (8:5) then compound ratio is 16 : 9 .

Componendo and Dividendo
Componendo and Dividendo states that If then .
See Questions and Answers for example.
Ques: Write a simple form of ratio 12:15.
(a) 4:5 (b) 4:3 (c) 5:4 (d) None of these
Example for Componendo and Dividendo
prove that ( Multiplying by 2 on both sides and dividing by 9 on both sides) (By Componendo and dividendo) (By Invertendo)Proportion
Equality of two ratio are said to be proportion.
If a : b= c : d then we write a : b : : c : d where a,b,c,d are in proportion. Here a and d are extremes and b and c are mean terms.
Formula is :
Products of extremes  =  Products of means 
(a * d)  =  (b *c ) 
Types of proportion
 Fourth proportion : If a : b = c : d then d is the fourth proportion.
 Third proportion : If a : b = b : c then c is the third proportion.
 Mean proportion : Mean proportion between a and b is .
Ques 1 : If a : b = 5 : 9 and b : c =4 : then find a : b : c.
(a) 20 : 63 : 36 (b) 22 :36 :63 (c) 20 :36 : 63 (d) none of these
Variation
 If x = ky and k is constant then we said that x is directly proportional to y and also x y.
 We say that x is inversely proportional to y, if xy = k for some constant k and we write ,x .
Important Note:
Ratio will be in simple form then the H.C.F. is 1.