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Home->Aptitude->Alligation or Mixture ->Formula/Rule 1

Alligation or Mixture :-

    Direct Formula / Rule 1 :

  • Theorem: The proportion in which sugar at Rs. x per kg must be mixed with rice at Rs. y per kg, so that the mixture be worth Rs. z a kg, is given by

    = ( y - z )
    z - x

  • Example :

  • The proportion in which sugar at Rs. 3.10 per kg must be mixed with sugar at Rs. 3.60 per kg, so that the mixture be worth Rs. 3.25 a kg ?

  • Detail Method : Let the required ratio be x. y.
     As per Question,
     310x + 360y = 325(x+y)
     or 310x + 360y = 325x + 325y
     325x - 310x = 360y - 325y
     150x = 350y
     15x = 35y
     3x = 7y
    = x : 7
    y3
     so x : y = 7 : 3    [here y goes to left side & 3 goes to right side]

  • Ailigation Method : By the rule of alligation we have :
    C.P.of 1 kg cheaper sugar C.P.of 1 kg dearer sugar
    (310 paise) Mean price
    (325 paise)
    (360 paise)
    35 15
    So, ratio of 1st and 2nd quantities = 35 : 15 = 7 : 3
    so, they must be mixed in the ratio of = 7 : 3

  • Quicker Method : Here you can use direct formula :
    = ( y - z )
    z - x
    = ( CP of dearer - Mean Price )
    Mean Price - CP of cheaper
    = ( 3.60 - 3.25 ) = ( 0.35 )
    3.25 - 3.100.15
    so, they must be mixed in the ratio of = 7 : 3


    Exercise :
  1. In what proportion must rice at Rs 21 per kg be mixed with rice at Rs 28 per kg, so.that the mixture be worth Rs. 25 a kg ?
  2. In what ratio, must coffee at Rs. 62 per kg Is mixed With coffee at Rs. 72 per kg so that the mixture must be worth RS. 64.50 per kg ?
  3. In what ratio must water be mixed with oil costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre ?
  4. Answers :
    1 = 5 : 4,   2 = 3 : 1,   3 = 1 : 2