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 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 9 :

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

• Example :

• A trader has 50 kg ofpulses, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. What is t e quantity sold at 18% profit?

• Detail Method :
Let the quantity sold at 18% profit be x kg. Then the quantity sold at 8% profit will be (50 - x) kg.
For a matter of convenience suppose that the price of pulse is 1 rupee per kg.
Then price of x kg pulse = Rs x and price of (50 - x) kg pulse = Rs (50 - x)
Now we get an equation,
18% of x + 8% of (50 - x)= 14% of 50
18x + 8(50 - x) = 14 X 50
10x = 300
∴ x = 30

• Ailigation Method :

 I Part II Part
 8% profit mean profit 14% 18% profit 4% 6%
= 4 : 6 = 2 : 3
Therefore the quantity sold at 18% profit  = 50 X 3 = 30 kg, 2 + 3

• Quicker Method : Here you can use direct formula :
 the required quantity = ( 14 - 8 ) X 50 18 - 8
 = 6 X 50 = 30 kg. 10

Exercise :
1. A trader has 25 kg of rice, part of which he sells at 4% profit and the rest at 9% profit. He gains 7% on the whole. What is the quantity sold at 9% profit?
2. A trader has 100 kg of wheat, part of which he sells at 16% profit and the rest at 36% profit. He gains 28% on the whole. What is the quantity sold at 36% profit?
3. A trader has 40 kg of pulses, part of which he sells at 10% profit and the rest at 20% profit. He gains 16% on the whole. What is the quantity sold at 20% profit?
4. Answers : 1 = 15 kg,   2 = 60 kg,   3 = 24 kg

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