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Home->Aptitude->Alligation or Mixture ->Formula/Rule 7

Alligation or Mixture :-

    Direct Formula / Rule 7 :

  • Theorem: A person has a liquid of Rs x per litre. The ratio in which water should be mixed in that liquid, so that after selling litre mixture at Rs y per litre he may get a profit of P%, is given by
    = ( y )
    (x - y) + ( p ) x
    100

  • Example :

  • A person has a chemical of Rs 25 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs 20/litre he may get a profit of 25%.

  • Detail Method :
    Let the ratio of chemical to water in the mixture be a : b.
    Cost price of the chemical is Rs 25 per litre
    ∴ cost price of a litre of the chemical = Rs 25
    Assume that the cost price of water be Rs 0 per litre
    Now, according to the question,
    Selling price of the mixture = Rs 20 per litre
    ∴ Selling price of (a + b) litres of the mixture
    = Rs (a + b) 20
    Cost price of (a + b) litres of the mixture
    = (a + b) X 20 X 100
    125
    (By the rule of fraction)
    = Rs (a + b) 16
    or,25 X a + 0 X b = (a + b) 16
    or, 9a = 16b
    or, a = 16
    b9
    So a : b = 16 : 9
    So Required ratio = 16 : 9.

  • Ailigation Method :
    In this question the alligation method is applicable on prices, so we should get the average price of mixture.
    SP of mixture = Rs 20/litre, profit = 25%
    ∴ average price = 20 X 100 = Rs 16/litre
    125
    Chemical Water
    25    16 0
    16 9
    ∴ Chemical : Water = 16 : 9

  • Quicker Method : Here you can use direct formula :
    reqd ratio = ( 20 )
    (25 - 20) + ( 25 ) X 25
    100
    = 80 = 16 = 16 : 9.
    459


    Exercise :
  1. A milk seller pays Rs 500 per kilolitre for his milk. He adds water to it and sells the mixture at 56 P a litre, thereby making altogether 40% profit. Find the proportion of water to milk which his customers receive.
  2. A person has a chemical of Rs 50 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs 40 per litre he may get a profit of 50%.
  3. A man buys milk at Rs 5 a litre and mixes it with water. By selling the mixture at Rs 4 a litre he gains 12 1/2 per cent on his outlay. How much water did each litre of the mixture contain?
  4. Answers : 1 = 1 : 4,   2 = 8 : 7,   3 = 13/45 litre