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

Direct Formula / Rule 24 :

• Theorem: There is a cask which contains 'L' litres of milk as cost price Rs x/litre. The amount of water, which should be added to the cask so that the cost of milk reduces to Rs y/litre, is given by  = L [ x - y ] litres. y

• Example :

• How much water must be added to a cask which contains 40 litres of milk at cost price Rs 3.5/litre so that the cost of milk reduces to Rs 2/litre?

• Detail Method :
Let the x litres of water be added to the the cask.
Cost price of 40 litres of milk = 40 X 3.5 = Rs 140.
According to the question,  = 140 = 2 or, 2x = 140 - 80 = 60 40 + x
So x = 30 litres.

• Ailigation Method :
We will apply the alligation on price of milk, water and mixture.
 Milk Water
 3.5 2 0 2 1.5
∴ ratio of milk and water should be 2 : 1.5 = 4 : 3.
∴ added water = 40/4 X 3 = 30 litres.

• Quicker Method : Here you can use direct formula :
required amount of water  = 40 [ 3.5 - 2 ] = 40 X 3/4 = 30 litres. 2

Exercise :
1. How much water must be added to 14 kilolitres of milk worth Rs 5.40 a litre so that the value of the mixture may be Rs 4.20 a litre?
2. How much chicory at Rs 24 a kg should be added to 15 kg of tea at Rs 60 a kg, as to make the mixture worth Rs 39 a kg?
3. How many bananas at 5 for Rs. 1.20 should be mixed with 300 bananas at 6 for Rs 2.10 so that they should all be worth Rs 3.60 a dozen?
4. Answers : 1 = 4 kilolitres,   2 = 21 kg,   3 = 250

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