Ratio, Proportion


  1. The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is









  1. View Hint View Answer Discuss in Forum

    Let the quantity of milk in the
    mixture = 7x litres and that of
    water = 5x litres.
    According to the question,

    7x
    =
    7
    5x + 158

    ⇒  56x = 35x + 105
    ⇒  56 x – 35 x = 105
    ⇒  21x = 105
    ⇒  x =
    105
    = 5
    21

    ∴  Required quantity of water
    = (5x + 15) litres
    = 5 × 5 + 15 = 40 litres

    Correct Option: B

    Let the quantity of milk in the
    mixture = 7x litres and that of
    water = 5x litres.
    According to the question,

    7x
    =
    7
    5x + 158

    ⇒  56x = 35x + 105
    ⇒  56 x – 35 x = 105
    ⇒  21x = 105
    ⇒  x =
    105
    = 5
    21

    ∴  Required quantity of water
    = (5x + 15) litres
    = 5 × 5 + 15 = 40 litres


  1. Vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4?









  1. View Hint View Answer Discuss in Forum

    First of all we write the fraction of milk present in three mixtures.

    In A;
    4
    and In B;
    5
    96

    In combination of A and B;
    5
    9

    From alligation rule,

    =
    5
    :
    1
    189

    ⇒ 
    5
    :
    2
    ⇒ 5 : 2
    1818

    So, ratio of
    A : B = 5 : 2

    Correct Option: C

    First of all we write the fraction of milk present in three mixtures.

    In A;
    4
    and In B;
    5
    96

    In combination of A and B;
    5
    9

    From alligation rule,

    =
    5
    :
    1
    189

    ⇒ 
    5
    :
    2
    ⇒ 5 : 2
    1818

    So, ratio of
    A : B = 5 : 2



  1. In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?









  1. View Hint View Answer Discuss in Forum

    Quantity of milk

    =
    7
    × 80 = 56 litres
    10

    Quantity of water
    =
    3
    × 80 = 24 litres
    10

    Let x litre water be added
    Then,  
    56
    =
    2
    24 + x1

    ⇒  24 + x = 28
    x = 4 litres

    Correct Option: D

    Quantity of milk

    =
    7
    × 80 = 56 litres
    10

    Quantity of water
    =
    3
    × 80 = 24 litres
    10

    Let x litre water be added
    Then,  
    56
    =
    2
    24 + x1

    ⇒  24 + x = 28
    x = 4 litres


  1. There is 81 litres pure milk in a container. One-third of milk is replaced by water in the container. Again one-third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?









  1. View Hint View Answer Discuss in Forum

    Quantity of milk in the last

    = 811 −
    27
    2 = 811 −
    1
    2
    813

    = 81 ×
    2
    ×
    2
    = 36
    33

    Quantity of water in the last
    = 81 – 36 = 45
    ∴  Ratio =
    36
    ×
    4
    = 4 : 5
    455

    Correct Option: D

    Quantity of milk in the last

    = 811 −
    27
    2 = 811 −
    1
    2
    813

    = 81 ×
    2
    ×
    2
    = 36
    33

    Quantity of water in the last
    = 81 – 36 = 45
    ∴  Ratio =
    36
    ×
    4
    = 4 : 5
    455



  1. A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?









  1. View Hint View Answer Discuss in Forum

    Let the barrel contain 4 litres of mixture.
    ∴  Wine = 3 litres
    Water = 1 litre
    Let x litre mixture is taken out.
    ∴  Wine in (4 – x) litres mixture

    =
    3
    (4 − x)
    4

    On adding x litres water, water in mixture
    = (4 − x) ×
    1
    + x
    4

    = 1 −
    x
    + x
    4

    =
    4 − x + 4x
    =
    4 + 3x
    44

    ∴ 
    3
    (4 − x) =
    4 + 3x
    44

    ⇒  3 −
    3x
    = 1 +
    3x
    44

    ⇒ 2 =
    6x
    4

    ⇒  x =
    2 × 4
    =
    4
    63

    ∴  Required answer =
    (4/3)
    =
    1
    43

    Correct Option: B

    Let the barrel contain 4 litres of mixture.
    ∴  Wine = 3 litres
    Water = 1 litre
    Let x litre mixture is taken out.
    ∴  Wine in (4 – x) litres mixture

    =
    3
    (4 − x)
    4

    On adding x litres water, water in mixture
    = (4 − x) ×
    1
    + x
    4

    = 1 −
    x
    + x
    4

    =
    4 − x + 4x
    =
    4 + 3x
    44

    ∴ 
    3
    (4 − x) =
    4 + 3x
    44

    ⇒  3 −
    3x
    = 1 +
    3x
    44

    ⇒ 2 =
    6x
    4

    ⇒  x =
    2 × 4
    =
    4
    63

    ∴  Required answer =
    (4/3)
    =
    1
    43