Alligation or Mixture

Alligation or Mixture

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Aptitude miscellaneous
  1. Rs. 1000 is lent out in two parts, one at 6 % simple interest and the other at 8 % simple interest. The yearly income is Rs. 75. The sum lent at 8 % is —








  1. View Hint View Answer Discuss in Forum

    According to question ,
    Given :- Total interest = Rs. 75

    Average rate =
    100 × 75
    		%
    1000 × 1
    Average Rate = 71 %
    2

    ∴ (Sum at 6%) : (Sum at 8%)
    =
    1
    		:
    3
    		= 1:3
    22

    Correct Option: C

    According to question ,
    Given :- Total interest = Rs. 75

    Average rate =
    100 × 75
    		%
    1000 × 1
    Average Rate = 71 %
    2

    ∴ (Sum at 6%) : (Sum at 8%)
    =
    1
    		:
    3
    		= 1:3
    22
    ∴ sum at 8% = Rs.1000 ×
    3
    4

    Hence , sum at 8 % = Rs. 750.

  1. A jar full of whisky contains 40 % of alcohol. A part of this whisky is replaced by another containing 19 % alcohol and now the percentage of alcohol was found to be 26. The quantity of whisky replaced is —








  1. View Hint View Answer Discuss in Forum

    Using the method of alligation ,
    Here , C1 = 40% , C2 = 19% and Mean cost Price ( M ) = 26%
    Required ratio = ( M - C2 ) : ( C1 - M ) = ( 26 - 19 ) : ( 40 - 26 )

    Correct Option: C

    Using the method of alligation ,
    Here , C1 = 40% , C2 = 19% and Mean cost Price ( M ) = 26%
    Required ratio = ( M - C2 ) : ( C1 - M ) = ( 26 - 19 ) : ( 40 - 26 )
    Required ratio = 7 : 14 = 1 : 2

    ∴ Required quantity =
    2
    3

  1. A mixture of 20 kg of spirit and water contains 10 % water. How much water must be added to this mixture to raise the percentage of water to 25 % ?








  1. View Hint View Answer Discuss in Forum

    As per the given question , we can say that
    In first mixture ,

    Water =
    10
    		× 20 = 2 kg
    100

    Correct Option: A

    As per the given question , we can say that
    In first mixture ,

    Water =
    10
    		× 20 = 2 kg
    100

    and Spirit = 18 kg
    In second mixture ,
    75 kg spirit is contained in a mixture of 100 kg .
    ∴ 18 kg spirit is contained in a mixture of
    100
    		× 18= 24kg
    75

    So, water to be added = (24 – 20) kg = 4 kg.

  1. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:








  1. View Hint View Answer Discuss in Forum

    Here first two varieties of tea are mixed in equal ratio.
    So their average price = (126 + 135) /2 = Rs. 130.50


    Correct Option: B

    Here first two varieties of tea are mixed in equal ratio.
    So their average price = (126 + 135) /2 = Rs. 130.50
    Let price of the third variety per kg be Rs. A; then now mixture is formed by two varieties one at Rs. 130.50 per kg and other at Rs. A per kg in the same ratio 2 : 2 i.e, 1 : 1
    By the rule of alligation,
    (A - 153) / (22.50) = 1
    ⇒ A – 153 = 22.50
    ∴ A = Rs. 175.50


  1. A container of 90 liters with two liquids A and B, 60% of liquid A and 30% of liquid B are taken out of the vessel. This leaves the container 40% empty. Find the initial quantity of both liquids.








  1. View Hint View Answer Discuss in Forum

    Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty.


    Correct Option: D

    Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty.
    Applying the rule of alligation, we get
    A : B = 10 : 20 or 1 : 2
    Quantity of liquid = 1 (1 + 2) × 90 = 30
    liters Quantity of liquid B = 90 – 30 = 60 liters.