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

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 - 25 4 2
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 + 4 10

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%

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