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Home->Aptitude->Alligation or Mixture ->Formula/Rule 20

Alligation or Mixture :-

    Direct Formula / Rule 20 :

  • Theorem: A man mixes M1 litres of milk at Rs x per litre with M2 litres at Rs y per litre. Amount of water, that should be added to make the average value of the mixture Rs z per litre, is given by
    = [ M1(x - z) + M2(y - z) ] litres.
    z

  • Example :

  • A man mixes 5 kilolitres of milk at Rs 600 per kilolitre with 6 kilolitres at Rs 540 per kilolitre. How many kilolitres of water should be added to make the average value of the mixture Rs 480 per kilolitre?

  • Detail Method :
    According to the question,
    Cost of 5 kilolitres of milk = 600 X 5 = Rs 3000
    Cost of 6 kilolitres of milk = 540 X 6 = Rs 3240
    Now, we suppose that x kilolitres of water is added.
    Total amount of the mixture = 5 + 6 + x = (11 + x) kilolitres.
    Total cost of the mixture = Rs 3000 + Rs 3240= Rs 6240
    From the question.
    = 6240 = 480
    11 + x
    or, 11 + x 6240 = 13
    480
    ∴ x = 2 kilolitres

  • Ailigation Method :
    Cost of milk when two qualities are mixed
    = 5 X 600 + 6 X 540 = Rs 6240 per kilolitre.
    5 + 611
    Cost of water = Rs 0/ kilolitre.
    So, First mixture (milk) Second mixture (water)
    6240/11 Average Speed
     480
    0
    480 960/11
    ∴ Ratio of milk and water = 480 : 960/11 = 1 : 2/11 = 11 : 2
    Which implies that 11 kilolitres of milk should be mixed with 2 kilolitres of water. Thus 2 kilolitres of water should be added.

  • Quicker Method : Here you can use direct formula :
    The required amount of water
    = 5 X (600 - 480) + 6 X (540 - 480)
    480
    = 5 X 120 + 6 X 60 = 960 = 2 kilolitres.
    480480


    Exercise :
  1. A man mixes 5 kilolitres of milk at Rs 6000 per kilolitre with 6 kilolitres at Rs 5400, and with sufficient water to make the average value Rs 4800 per kilolitre. How many kilolitres of water has he added?
  2. A man mixes 6 kilolitres of milk at Rs 650 per kilolitre with 7 kilolitres at Rs 600, and with sufficient water to make the average value Rs 540 per kilolitre. How many kilolitres of water has he added?
  3. A man mixes 6 kilolitres of milk at Rs 325 per kilolitre with 9 kilolitres at Rs 300, and with sufficient water to make the average value Rs 270 per kilolitre. How many kilolitres of water has he added?
  4. Answers : 1 = 2 kilolitres,   2 = 2 kilolitres,   3 = 2 2/9 kilolitres