Ratio, Proportion


  1. In a mixture of 25 litres, the ratio of acid to water is 4 : 1. Another 3 litres of water is added to the mixture. The ratio of acid to water in the new mixture is









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    In 25 litres of mixture,

    Acid =
    4
    × 25 = 20 litres
    5

    Water = 5 litres.
    After adding 3 litres of water, quantity becomes 8 litres
    ∴  New ratio = 20 : 8 = 5 : 2

    Correct Option: A

    In 25 litres of mixture,

    Acid =
    4
    × 25 = 20 litres
    5

    Water = 5 litres.
    After adding 3 litres of water, quantity becomes 8 litres
    ∴  New ratio = 20 : 8 = 5 : 2


  1. The ratio of the quantities of an acid and water in a mixture is 1 : 3. If 5 litres of acid is further added to the mixture, the new ratio becomes 1 : 2. The quantity of new mixture (in litres) is









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    Let the quantity of acid in original mixture be x litre and that of water be 3x litres.

    ∴ 
    x + 5
    =
    1
    3x2

    ⇒  2x + 10 = 3x
    ⇒  x = 10
    ∴  Quantity of new mixture
    = 4x + 5 = 45 litres

    Correct Option: D

    Let the quantity of acid in original mixture be x litre and that of water be 3x litres.

    ∴ 
    x + 5
    =
    1
    3x2

    ⇒  2x + 10 = 3x
    ⇒  x = 10
    ∴  Quantity of new mixture
    = 4x + 5 = 45 litres



  1. The ratio of the volume of water and glycerine in 240cc of a mixture is 1 : 3. The quantity of water (in cc) that should be added to the mixture so that the new ratio of the volumes of water and glycerine becomes 2:3 is









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    In the original mixture, water = 60 cc
    Glycerine = 180 cc
    Let x cc of water be mixed.

    ∴ 
    60 + x
    =
    2
    1803

    ⇒  180 + 3x = 360
    ⇒  3x = 360 – 180 = 180
    ∴  x =
    180
    = 60 cc
    3

    Correct Option: B

    In the original mixture, water = 60 cc
    Glycerine = 180 cc
    Let x cc of water be mixed.

    ∴ 
    60 + x
    =
    2
    1803

    ⇒  180 + 3x = 360
    ⇒  3x = 360 – 180 = 180
    ∴  x =
    180
    = 60 cc
    3


  1. A mixture contains wine and water in the ratio 3 : 2 and another mixutre contains them in the ratio 4 : 5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of wine and water ?









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    ∴  Required ratio =
    1
    :
    1
    1810

    = 5 : 9
    = 3 :
    9
    × 3 = 3 : 5
    2
    55

    ∴  5
    2
    litre must be added
    5

    Correct Option: A


    ∴  Required ratio =
    1
    :
    1
    1810

    = 5 : 9
    = 3 :
    9
    × 3 = 3 : 5
    2
    55

    ∴  5
    2
    litre must be added
    5



  1. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 5 : 3 and 5 : 11 respectively. Equal quantities of these alloys are melted to form a third alloy C. The ratio of gold and copper in the alloy C is









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    Let 1 kg of each of the alloys A and B be mixed together.
    In alloy A,

    Quantity of gold =
    5
    kg.
    8

    Quantity of copper =
    3
    kg.
    8

    In alloy B,
    Quantity of gold =
    5
    kg.
    16

    Quantity of copper =
    11
    kg.
    16

    =
    5
    +
    5
    :
    3
    +
    11
    816816

    =
    15
    :
    17
    1616

    = 15 :17

    Correct Option: C

    Let 1 kg of each of the alloys A and B be mixed together.
    In alloy A,

    Quantity of gold =
    5
    kg.
    8

    Quantity of copper =
    3
    kg.
    8

    In alloy B,
    Quantity of gold =
    5
    kg.
    16

    Quantity of copper =
    11
    kg.
    16

    =
    5
    +
    5
    :
    3
    +
    11
    816816

    =
    15
    :
    17
    1616

    = 15 :17