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Home->Aptitude->Alligation or Mixture ->Formula/Rule 25

Alligation or Mixture :-

    Direct Formula / Rule 25 :

  • Theorem: One type of liquid contains x% of A, the other contains y% of A. A can is filled with n parts of the first liquid and m parts of the second liquid. Then the percentage of liquid A in the new mixture is given by
    = [ nx + my ] percent.
    (n + m)

  • Example :

  • One type of liquid contains 25% of milk, the other contains 30% of milk. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of milk in the new mixture.

  • Detail Method :
    The reqd. percentage of milk in the new mixture
    = Quantity of milk in the new mixture X 100
    Quantity of the new mixture
    = 6 parts of 25% milk + 4 parts of 30% milk X 100
    (6 parts + 4 parts)of the liquid
    = 6 X 25/100 + 4 X 30/100 X 100
    10
    = (15 + 12) = 27

  • Ailigation Method :
    25        x 30
    6 4
    = 30 - x = 6 = 3
    x - 2542
    or, 60 - 2x = 3x - 75
    or, 5x = 60 + 75
    ∴ x = 27%

  • Quicker Method : Here you can use direct formula :
    required answer = 6 X 25 + 4 X 30 = 270 = 27%.
    6 + 410


    Exercise :
  1. A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20 litres of the first solution to make a solution of 10% sugar?
  2. One type of liquid contains 15% of milk, the other contains 20% of milk. A can is filled with 4 parts of the first liquid and 11 parts of the second liquid. Find the percentage of milk in the new mixture.
  3. One type of liquid contains 12 1/2% of milk, the other contains 15% of milk. A can is filled with 8 parts of the first liquid and 12 parts of the second liquid. Find the percentage of milk in the new mixture.
  4. Answers : 1 = 20,   2 = 18 2/3%,   3 = 14%