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Ratio and proportion short tricks




 अनुपात समानुपात शार्ट ट्रिक्स Ratio and Proportion

In this article we are going to share some important and interesting short tricks of ratio and proportions questions in Hindi as well as English questions. With the help of this tricks students will learn how to solve ratio and proportions problems in very few minutes. It's very important for those candidates who are appearing in various competitive examination.
Ratio:-  
            The division of two numbers is known as Ratio. It is denoted by (:).
            Example: 5:7 or 5/7 , 2:3 or 2/3 etc.

Type and Ratio Short Trick 1:

If A : B = X : Y and B : C = P : Q ,then:-
  1. A : C = X x P : Y x Q
  2. A : B : C = (X : Y) x P :Y x Q = X x P : Y x P : Y x Q
                 or        A    :    B   :   C
                            X    :   Y
                                \      |      \  
                                      P     :    Q
                        ___________________
                         X x P : Y x P : Y x Q
   Example: If  A : B = 4 : 5 and B : C = 6 : 7 then, find value of A : C ?




Type and Ratio Short Trick of  2:

              If A : B = X : Y , B : C = P : Q and C : D = M : N then:-
  1. A : D = X x P x M : Y x Q x N
  2. A : B : C : D = (XP : YP : YQ) x M : Y x Q x N                                                                                       = XPM : YPM : YQM : YQN


Example:  If A : B = 3 : 4 , B : C = 8 : 9 and C : D = 12 : 13 then, find value of A : D ?



Type and Ratio Short Trick 3:

  1. If  A : B : C : D = W : X : Y : Z and D : E = M : N  then
                                     and
     2. If  A : B : C : D = W : X : Y : Z and D : E : F = L : M : N  then


Example: If  A : B : C : D = 3 : 2 : 5 : 4 and D : E = 3 : 5  then find A : B : C : D : E ?




Type and Ratio Short Trick 4:

  1. First proportion       ,    a = (b x c) / d
  2. Second proportion    ,    b = (a x d) / c
  3. Third proportion      ,     c = (a x d) / b
  4. Fourth proportion     ,     d = (b x c)/ a
Example:  ? : 3 : : 15 : 9




Type and Ratio Short Trick 5:

By expiration a : b : : b : c :-

  1. First proportion       ,    a = (b^2) / c
  2. Second proportion    ,    b = (ac)^(1/2)
  3. Third proportion      ,     c = (b^2) / a

Example:Find the first proportion of 6 and 9

Type and Ratio Shortrick 6:


If X has to divide in ratio of P and between Q has to divide into ratio of A : B, then

  1. Part of P = {a / (a+b)} x X
  2. Part of Q = {b / (a+b)} x X
  3. Difference between parts of P and Q = {(a-b) / (a+b)} x X          [where   a > b] 
Example:If 320 rs has to divide in ratio of A and between B has to divide into ratio of 3 : 5, then find part of A , part of B and difference between A and B.





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Type and Ratio Short Trick 7:


If ratio of parts of P and Q is a : b and difference between there parts is X, then

  1. Part of P = {a / (a-b)} x X
  2. Part of Q = {b / (a-b)} x X
  3. Difference between parts of P and Q = {(a+b) / (a-b)} x X           [where   a > b] 
Example:The ratio between part of Amar and Suresh is 3 : 2. If part of Amar is more then Suresh by 500 rs , then find part of Suresh.








Type and Ratio Short Trick 8:

            If ratio of parts of P and Q is a : b and part of P is X, then

  1. Part of Q                  = (b / a) x X
  2. Total part of P and Q = (a + b) x X
  3. Difference between parts of P and Q = {(a-b) / a} x X 

Example:How much zinc should be added to 24 gram of copper, such that there ration will become 9:4





Type and Ratio Short Trick 9:


                     When there will be ratio of a : b : c in P , Q and R



   1. If X is part of P,


  • Part of Q     =    (b/a) x X
  • Part of R     =    (c/a) x X
  • Difference between parts of Q and R = {(b-c)/a} x X       ,[where b>c]
  • Total part of P,Q and R = {(a+b+c)/a} x X

   2. If total part of P,Q and R will be X,


  • Part of P,Q and R respectively :- a/(a+b+c) x X , b/(a+b+c) x X and c/(a+b+c) x X
  • Difference between parts of P and Q = (a-b) / (a+b+c) x X  ,    [where a>b]
  • Difference between parts of Q and R = (b-c) / (a+b+c) x X  ,    [where b>c]

   3. If difference between parts of P and Q is X,

  • Part of R     =    {c / (a-b)} x X,                           [where a>b]
  • Total part of P,Q and R = {(a+b+c) / (a-b)} x X ,   [where a>b]
  • Difference between parts of Q and R = (b-c) x X    [where a>b and b>c]
Example: The ratio of pencil , pan and book in any shop is 10 : 2 : 3 , If there is 120 pencils then find the number of book?











Type and Ratio Short Trick 10:


  Example: The two mixture of gold and copper is A and B. In A the ratio of gold and copper is 7:2 , there as in B  the ratio of gold and copper is 7:11. In by mixing A and B in same quantity to form a new metal C, then what will be the ratio of gold and copper in C?










Type and Ratio Short Trick 11:


Example: Ramnath have some cows and cock. If total number of heads is 55 and total number of legs is 160 ,then how much cows did he have?













Type and Ratio Short Trick12:


Example: 












Type and Ratio Short Trick 13:


Example: In a bag note of 20 rs, 10 rs and 5 rs is in ratio of 3:4:5. If there is total 1000 rs, then find the number of notes of 5 rs?










Type and Ratio Short Trick 14:


Example: 










Type and Trick 15:


Example: 














 Questions asked in competitive exams



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