Alligation or Mixture

Alligation or Mixture

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Aptitude miscellaneous
  1. A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?








  1. View Hint View Answer Discuss in Forum

    Let A liters wine cask hold originally, then
    A[1 - (8 / A )]4 / A = 16 / 81

    Correct Option: C

    Let A liters wine cask hold originally, then
    A[1 - (8 / A)]4 / A = 16 / 81
    ⇒ (1 - (8 / A))4 = (2 / 3 )4
    ⇒ (1 - (8 / A)) = (2 / 3)
    ⇒ (8 / A) = (1 - (2 /3))
    ⇒ (8 / A) = (1 / 3)
    ∴ A = 24 liters

  1. A shopkeeper has 100 kgs of tea. He sells a part of it at 20% profit and the rest at 5% loss. If his overall profit is 10%, find the quantity for each part.








  1. View Hint View Answer Discuss in Forum

    As per figure, we can calculate as below.
    Quantity sold at 20% profit = 3 / (3 + 2) × 100 = 60 kgs.
    Quantity sold at 5% loss = (100 – 60) = 40 kgs.


    Correct Option: A

    As per figure, we can calculate as below.
    Quantity sold at 20% profit = 3 / (3 + 2) × 100 = 60 kgs.
    Quantity sold at 5% loss = (100 – 60) = 40 kgs.


  1. In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?








  1. View Hint View Answer Discuss in Forum

    S.P. of 1 kg mixture = Rs. 68.20, Gain% = 10%
    Hence, C.P. of 1 kg mixture = (100 / 110) x Rs. 68 20 . = Rs. 62


    Correct Option: D

    S.P. of 1 kg mixture = Rs. 68.20, Gain % = 10 %
    Hence, C.P. of 1 kg mixture = (100 / 110) x 68 20 . = Rs. 62
    By the rule of alligation
    Hence, required ratio = 3 : 2


  1. In a mixture of 45 liters, the ratio of milk and water is 4:1. How much water must be added to make the mixture ratio 3:2 ?








  1. View Hint View Answer Discuss in Forum

    Let us assume the ratio factor is x.
    According to question,
    Quantity of milk = 4x liters and Quantity of Water = x liters.
    According to question,
    4x + x = 45
    Let y liters of water be added to make the ratio 3:2
    Then, 36/(9 + y) = 3/2
    Solve the above both equation to get the answer.

    Correct Option: C

    Let us assume the ratio factor is x.
    According to question,
    Quantity of milk = 4x liters and Quantity of Water = x liters.
    According to question,
    4x + x = 45
    ⇒ 5x = 45
    ⇒ x = 9
    Quantity of milk = 4x = 9 x 4 = 36 liters
    Quantity of water = x = 9 liters
    Let y liters of water be added to make the ratio 3:2
    Then,
    36/(9 + y) = 3/2
    ⇒ 72 = 27 + 3y
    ⇒ y = 15 liters
    If you add 15 liters of water, the ratio will become 3:2.

  1. A sum of Rs. 70 is divided among 10 children. Each boy gets Rs. 10 whereas a girl gets Rs. 5. If the number of boys is 4, find the number of girls.








  1. View Hint View Answer Discuss in Forum

    Number of girls / Number of boys = (3 / 2)


    Correct Option: A

    Number of girls / Number of boys = (3 / 2)
    Number of girls = (3 / 2) × 4 = 6