Alligation and Mixture-Short Tricks 1

    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
    y 3

     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 – 3.10 0.15

    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

Alligation and Mixture-Short Tricks 2
GK- Full list of Padma Awardees 2017

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