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Home->Aptitude->Alligation or Mixture ->Formula/Rule 4

Alligation or Mixture :-

    Direct Formula / Rule 4 :

  • Theorem: The proportion in which water must be mixed with spirit to gain or to lose x% by selling it at cost price is given by
    = ( x )
    100

  • Example :

  • In what proportion must water be mixed with spirit to gain 16 2/3% by selling it at cost price?

  • Detail Method : Let the required proportion of water to spirit be a : b and the cost price of spirit be Rs x per litre.
    As per the question,
    Selling price of the mixture = Rs x per litre.
    Cost price of the mixture  
    = x X 100
    x X 100
    100
    = Rs 6x = per litre.
    7
    Now, assume that the cost price of water = Rs 0 per litre.
    ∴ (a X 0 + b X x) = (a + b) 6x
    7
    or, bx = (a + b) = 6 x
    7
    or, b ( 1 - 6 ) = 6a
    7 7
    or, b = 6a
    7 7
    or, a = 1
    b 6
    ∴ required ratio = 1: 6

  • Ailigation Method :
    Let CP of sprit be Re 1 per litre.
    Then SP of 1 litre o f mixture = Rs 1.
    Gain = 16 2 %
    3
    CP of 1 litre of mixture = Rs ( 100 X 3 X 1 ) = Rs 6
    350 7
    CP of 1 litre water CP of 1 litre pure spirit
    (Rs 0) Mean price
       Rs 6/7
    (Rs 1)
    1/7 6/7
    Quantity of water = 1/7 = 1
    Quantity of spirit6/76
    or Ratio of water and spirit = 1 : 6.

  • Quicker Method : Here you can use direct formula :

    the required proportion = 50 = 1 : 6
    300


    Exercise :
  1. In what proportion must water be mixed with spirit to gain 33 1/3%by selling it at cost price?
  2. In what proportion must water be mixed with spirit to gain 16% by selling it at cost price?
  3. In what proportion must water be mixed with spirit to gain 25% by selling it at cost price?
  4. Answers : 1 = 1 : 3,   2 = 4 : 25,   3 = 1 : 4