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Home->Aptitude->Alligation or Mixture ->Formula/Rule 10

Alligation or Mixture :-

    Direct Formula / Rule 10 :

  • Theorem: A trader has N kg of a certain item, a part of which he sells at x% profit and the rest of y% loss. He gains P% on the whole
    Then the quantity sold at x% profit is = ( P + y ) N Kg
    x + y
    and the quantity sold at y% loss is = ( x - P ) N Kg
    x + y

  • Example :

  • A trader has 50 kg of rice, a part ofwhich he sells at 10% profit and the rest at 5% loss. He gains 7% on the whole. What is the quantity sold at 10% gain and 5% loss?

  • Detail Method :
    Let the quantity sold at 10% profit be x kg.
    Then the quantity sold at 5% loss will be (50 - x) kg.
    For a matter of convenience suppose that the price of rice is 1 rupee per kg.
    Then price of x kg rice = Rs x and price of (50 - x) kg rice = Rs (50 - x)
    Now we get an equation,
    10% profit of x + 5% loss of (50 - x) = 7% gain of 50
    or, 10% of x - 5% of (50 - x) = 7% of 50
    or, 10x-250 +5x =350
    ∴ x = 40 kg and (50 - x)= 50 - 40 = 10 kg.
    Therefore, the quantity sold at 10% profit = 40 kg and
    the quantity sold at 5% loss = 50 - 40 = 10 kg.

  • Ailigation Method :

    I Part II Part
    10       7 (-)5
    12 3
    Ratio of quantities sold at 10% profit and 5% loss
    = 12 : 3 = 4 : 1
    Therefore, the quantity sold at 10% profit
    = 50 X 4 = 40 kg,
    4 + 1
    and the quantity sold at 5% loss = 50 - 40 = 10 kg.
    Note: Whenever there is loss, take the negative value. Here, difference between 7 and (-5) = 7 - (-5) = 7 + 5 = 12. Never take the difference that counts negative value.

  • Quicker Method : Here you can use direct formula :
    Quantity sold at 10% profit = ( 7 + 5 ) X 50
    10 + 5
    = 12 X 50 = 40 kg.
    15
    Quantity sold at 5% loss = ( 10 - 7 ) X 50 = 10 kg.
    10 + 5


    Exercise :
  1. A trader has 90 kg of pulse, a part of which he sells at 20% profit and the rest at 10% loss. He gains 14% on the whole. What is the quantity sold at 20% gain and 10% loss?
  2. A trader has 45 kg of wheat, a part of which he sells at 30% profit and the rest at 15% loss. He gains 21% on the whole. What is the quantity sold at 30% gain and 15% loss?
  3. A trader has 40 kg of tea, a part of which he sells at 12% profit and the rest at 8% loss. He gains 9% on the whole. What is the quantity sold at 12% gain and 8% loss?
  4. Answers : 1 = 72 kg, 18 kg,   2 = 36 kg, 9 kg,   3 = 34 kg, 6 kg