# Ratio & Proportion Notes, Tricks, Questions and Answers

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 examplesQuestions & Answers for MCQs i.e. Objective Questions. Also these Study Notes can be downloaded in PDF from the button provided above.

# 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)”.

Also Read:  Simplification Notes-Tricks & Question

Example:-$\frac { 4 }{ 5 }$ is a ratio where 4 is numerator and 5 is denominator.

Note:- Multiplication and division of each term of a ratio by non-zero ratio will not affect on the ratio.

Example :- 4 : 3 = 8 : 6 = 12 : 9 etc.

## Types of ratio

1. ### Duplicate ratio

If ratio is a : b then duplicate ratio is ${a }^{2}$ : ${b }^{2}$.
Example: Ratio is 4 : 5 then duplicate ratio is 16 : 25.

2. ### Sub-duplicate ratio

If ratio is a : b then sub-duplicate ratio is $\sqrt { a }$ : $\sqrt { b }$.

Example : Ratio is 25 : 36 then sub-duplicate is 5 : 6.

3. ### Triplicate ratio

If ratio is a : b then triplicate ratio is ${a}^{3} : {b}^{3}$.

Example: Ratio is 5 : 6 then triplicate ratio is 125 : 216.

4. ### Sub-triplicate ratio

If ratio is a : b then sub-triplicate ratio is ${ a }^{ 1/3 }$ : ${ b }^{ 1/3 }$.

Example: Ratio is 64 : 125 then sub-triplicate is 4 : 5.

5. ### Comparison of ratio

If (a : b ) > (c : d )$\Leftrightarrow$ $\frac { a }{ b } > \frac { c }{ d }$.

Example: Which is greater ratio –$\frac { 4 }{ 5 }$ and$\frac { 2 }{ 3 }$.

Answer is $\frac { 4 }{ 5 }$.

6. ### 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 .

7. ### Componendo and Dividendo

Componendo and Dividendo states that If $\frac { a }{ b } =\frac { c }{ d }$ then $\frac { a+b }{ a-b} =\frac { c+d }{c-d }$.

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

$If\frac { a }{ b } =\frac { c }{ d }$ prove that$\frac { 2a-9b }{ 2a+9b } =\frac { 2c-9d }{ 2c+9d }$ $\frac { a }{ b } =\frac { c }{ d }$$\frac { 2a }{ 9b } =\frac { 2c }{ 9d }$ ( Multiplying by 2 on both sides and dividing by 9 on both sides)

$\frac { 2a+9b}{2a- 9b } =\frac { 2c+9d }{2c- 9d }$(By Componendo and dividendo)

$\frac { 2a-9b}{2a+ 9b } =\frac { 2c-9d }{2c+ 9d }$(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

1. Fourth proportion :- If a : b = c : d  then d is the fourth proportion.
2. Third proportion :- If a : b = b : c then c is the third proportion.
3. Mean proportion :- Mean proportion between a and b is $\sqrt { ab }$.

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

1. If x = ky and k is constant then we said that x is directly proportional to y and also x$\propto$ y.
2. We say that x is inversely proportional to y, if xy = k for some constant k and we write ,x $\propto$ $\frac { 1 }{ y }$.

# Important Note:

Ratio will be in simple form then the H.C.F. is 1.

Updated: August 9, 2016 — 7:34 am
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