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Home->Aptitude->Alligation or Mixture ->Formula/Rule 16

Alligation or Mixture :-

    Direct Formula / Rule 16 :

  • Theorem: L litres of a mixture contains two liquids A and B in the ratio a : b. The amount of liquid B, that is added to get a new mixture containing liquid A and B in the ratio x : y, is given by
    = [ ( y/x ) - ( 1 ) ] L litres.
    1 + b/a1 + a/b

  • Example :

  • 729 litres of a mixture contains milk and water in the ratio 7 : 2. How much water is to be added to get a new mixture containing milk and water in the ratio 7 : 3 ?

  • Detail Method :
    Let the amount of water be x litres.
    The original mixture contains ( 729 X 7 ) litres of milk
    7 + 2
    and ( 729 X 2 ) litres of water.
    7 + 2
    Now, from the question,
    x litres of water is added. Therefore = 729 X 7/9 = 7
    729 X 2/9 + x3
    or, 729 X 7 X 3 = 729 X 2 X 7 + 9 X 7x
    or, 63x = 7 X 729
    So x = 7 X 729 = 81 litres
    63

  • Ailigation Method :
    Method I. Percentage
    Change the ratio into percentage.
    % of water in the original mixture
    = 2 X 100 = 200/9%
    7 + 2
    % of water in the resulting mixture
    = 3 X 100 = 30%
    7 + 3
    200/9%        30% 100%
    70% 70/9%
    Therefore, the ratio in which the mixture and water are to be added is 1 : 1/9 or 9 : 1
    Then quantity of water to be added
    = 729 X 1 = 81 litres.
    9
    Method II. Fractional
    Change the ratio into fraction.
    Fraction of water in the original mixture = 2
    9
    Fraction of water in the resulting mixture = 3
    10
    So,
    2/9        3/10 1
    7/10 7/90
    Therefore, the ratio in which the mixture and water are to be added is
    = 7 : 7 = 1 : 1/9 = 9 : 1
    1090
    Then quantity of water to be added to the mixture
    and quantity of A in the jar = 729 = 81 litres.
    9

  • Quicker Method : Here you can use direct formula :
    = [ ( 3/7 ) - ( 1 ) ] X 729
    1 + 2/71 + 7/2
    = [3/7 X 7/9 - 2/9] X 729
    = (1/3 - 2/9) X 729 = 729/9 = 81 litres.


    Exercise :
  1. 56 litres of a mixture contains milk and water in the ratio 5 : 2. HOW much water is to be added to get a new mixture containing milk and water in the ratio 5 : 3 ?
  2. 36 litres of a mixture contains milk and water in the ratio 2 : 1. How much water is to be added to get a new mixture containing milk and water in the ratio I : 1 ?
  3. 25 litres of a mixture contains milk and water in the ratio 3 : 2. How much water is to be added to get a new mixture containing, milk and water in the ratio 3 : 4 ?
  4. Answers : 1 = 8 litres,   2 = 12 litres,   3 = 10 litres