Ratio, Proportion


  1. A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :









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    Number of brown socks = x
    Price of brown socks = ₹ y per pair
    Price of black socks = ₹ 2y per pair
    ∴  4y + x × 2y

    =
    150
    (4 × 2y + xy)
    100

    ⇒ 4 + 2x =
    3
    (8 + x)
    2

    ⇒  8 + 4x = 24 + 3x
    ⇒  x = 24 – 8 = 16
    ∴  Required ratio = 4 : 16
    = 1 : 4

    Correct Option: B

    Number of brown socks = x
    Price of brown socks = ₹ y per pair
    Price of black socks = ₹ 2y per pair
    ∴  4y + x × 2y

    =
    150
    (4 × 2y + xy)
    100

    ⇒ 4 + 2x =
    3
    (8 + x)
    2

    ⇒  8 + 4x = 24 + 3x
    ⇒  x = 24 – 8 = 16
    ∴  Required ratio = 4 : 16
    = 1 : 4


  1. A milkman makes 20% profit by selling milk mixed with water at 9 per litre. If the cost price of 1 litre pure milk is 10, then the ratio of milk and water in the mixture is









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    Milk : Water = K : 1
    ∴  S.P. = (K + 1) × 9
    C.P. = 10K
    Gain = 9 – K

    Gain % =
    9 − K
    × 100
    10K

    ⇒ 
    9 − K
    × 100 = 20
    10K

    ⇒  90 – 10K = 20K
    ⇒  30K = 90 ⇒ K = 3
    ∴  Ratio = 3 : 1

    Correct Option: A

    Milk : Water = K : 1
    ∴  S.P. = (K + 1) × 9
    C.P. = 10K
    Gain = 9 – K

    Gain % =
    9 − K
    × 100
    10K

    ⇒ 
    9 − K
    × 100 = 20
    10K

    ⇒  90 – 10K = 20K
    ⇒  30K = 90 ⇒ K = 3
    ∴  Ratio = 3 : 1



  1. There is a ratio of 5 : 4 between two numbers. If 40 per cent of the first is 12, then 50% of the
    second number is









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    Let numbers = 5x and 4x

    ∴  5x ×
    40
    = 12
    100

    ⇒  2x = 12 ⇒ x = 6 and
    Second number = 6 × 4 = 24
    ∴  50% of 24 = 24 ×
    50
    = 12
    100

    Correct Option: A

    Let numbers = 5x and 4x

    ∴  5x ×
    40
    = 12
    100

    ⇒  2x = 12 ⇒ x = 6 and
    Second number = 6 × 4 = 24
    ∴  50% of 24 = 24 ×
    50
    = 12
    100


  1. The reciprocals of the squares of the numbers
    1
    1
    and 1
    1
    . are in the ratio
    23









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    Ratio of the squares of
    3
    and
    4
    23

    =
    9
    :
    16
    49

    Ratio of their reciprocals
    =
    4
    :
    9
    916

    = 64 : 81

    Correct Option: A

    Ratio of the squares of
    3
    and
    4
    23

    =
    9
    :
    16
    49

    Ratio of their reciprocals
    =
    4
    :
    9
    916

    = 64 : 81



  1. Rs. 782 is divided into three parts in the ratio
    1
    :
    2
    :
    3
    , the first part is
    234









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    A : B : C =
    1
    :
    2
    :
    3
    234

    =
    1
    × 12 :
    2
    × 12 :
    3
    × 12
    234

    = 6 : 8 : 9
    Sum of the terms of ratio
    = 6 + 8 + 9 = 23
    ∴  First part
    = Rs.
    6
    × 782 = Rs. 204
    23

    Correct Option: B

    A : B : C =
    1
    :
    2
    :
    3
    234

    =
    1
    × 12 :
    2
    × 12 :
    3
    × 12
    234

    = 6 : 8 : 9
    Sum of the terms of ratio
    = 6 + 8 + 9 = 23
    ∴  First part
    = Rs.
    6
    × 782 = Rs. 204
    23