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Home->Aptitude->Alligation or Mixture ->Formula/Rule 24

Alligation or Mixture :-

    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