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Home->Aptitude->Alligation or Mixture ->Formula/Rule 22

Alligation or Mixture :-

    Direct Formula / Rule 22 :

  • Theorem: If a person buys n kg of an item at the rate of Rs P per kg. If he sells m kg at a profit of x%, then the rate per kg, at which he should sell the remaining to get a profit of y% on the total deal, is given by Rs P
    = [ 1 + ny - mx ]
    (n - m)100

  • Example :

  • Jayshree purchased 150 kg of wheat at the rate of Rs 7 per kg. She sold 50 kg at a profit of 10%. At what rate per kg should she sell the remaining to get a profit of 20% on the total deal?

  • Detail Method :
    Selling price of 150 kg wheat at 20% Profit
    = 150 X 7 (120/100) = Rs 1260
    Selling price of 50 kg wheat at 10% profit
    = 50 X 7 (110/100) = Rs 385
    So selling price per kg of remining 100 kg wheat
    = 1260 - 385 = Rs 8.75
    100

  • Ailigation Method :
    Selling price per kg at 10% profit = Rs 7.70 Selling price per kg at 20% profit = Rs 8.40 Now, the two lots are in ratio = 1 : 2
    7.7        8.4 x
    1 2
    = 8.4 - 7.7 = 2
    x - 8.41
    x - 8.4 = 0.7
    2
    x - 8.4 = 0.35
    x = 8.75

  • Quicker Method : Here you can use direct formula :
    the required answer
    = [ 150 X 20 - 50 X 10 + 1 ] X 7
    (150 - 50) X 100
    = [ 3000 - 500 + 1 ] X 7
    100 X 100
    = 5/4 X 7 = 35/4 = Rs 8.75 per kg.


    Exercise :
  1. Sugandha purchased 160 kg of rice at the rate of Rs 25 per kg. She sold 60 kg at a profit of 20%. At what rate per kg should she sell the remaining to get a profit of 30% on the total deal?
  2. Sunanda purchased 80 kg of wheat at the rate of Rs 10 per kg She sold 30 kg at a profit of 10%. At what rate per kg should she sell the remaining to get a profit of 15% on the total deal ?
  3. Answers : 1 = Rs 34,   2 = Rs 11.8