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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:  Average Notes Tricks Shortcuts

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

Answer

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

Answer

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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