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Home->Aptitude->Alligation or Mixture ->Formula/Rule 18

Alligation or Mixture :-

    Direct Formula / Rule 18 :

  • Theorem: If M kg of mixture, of which is a/b and the rest is B, be mixed with N kg of metal, of which is x/y and the rest is B, then the ratio of A to B in the mixture is given by
    = [
    M a + N x
    by
    ]
    M ( 1 - a ) + N ( 1 - x )
    by

  • Example :

  • If 2 kg of metal, of which 1/3 is zinc and the rest of copper, be mixed with 3 kg of metal, of which 1/4 is zinc and the rest is copper, what is the ratio of zinc to copper in the mixture?

  • Detail Method :
    Quantity of zinc in the mixture
    = 2(1/3)+3(1/4) = 2/3+3/4 = 8+9/12 = 17/12
    Quantity of copper in the metal
    = 3+2-17/12 = 5-17/12 = 43/12
    So ratio = 17/12 : 43/12 = 17 : 43

  • Quicker Method : Here you can use direct formula :
    the required ratio
    = [
    2 X 1 + 3 1
    34
    ]
    2 ( 1 - 1 ) + 3 ( 1 - 1 )
    34
    = 2/3 + 3/4 = 17 : 43.
    4/3 + 9/4


    Exercise :
  1. If 1 kg of metal of which 1/3 is zinc and the rest copper be mixed with 2 kg of metal of which 1/4 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
  2. If 4 kg of metal of which 1/4 is zinc and the rest copper be 1 mixed with 5 kg of metal of which 1/5 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
  3. If 5 kg of metal of which 3/5 is zinc and the rest copper be mixed with 3 kg of metal of which 2/3 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
  4. Answers : 1 = 5 : 13,   2 = 2 : 7,   3 = 5 : 3