Ratio, Proportion


  1. If x : y = 3 : 2, then the ratio 2x2 + 3y2 : 3x2 – 2y2 is equal to :









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    x : y = 3 : 2
    ⇒  x2 : y2 = 9 : 4

    ∴ 
    2x2 + 3y2
    3x2 − 2y2

    = 2
    x2
    + 3
    y2
    3
    x2
    − 2
    y2

    = 2 ×
    9
    + 3
    4
    3 ×
    9
    − 2
    4


    =
    18 + 2
    4
    27 − 8
    4

    = 30 : 19

    Correct Option: C

    x : y = 3 : 2
    ⇒  x2 : y2 = 9 : 4

    ∴ 
    2x2 + 3y2
    3x2 − 2y2

    = 2
    x2
    + 3
    y2
    3
    x2
    − 2
    y2

    = 2 ×
    9
    + 3
    4
    3 ×
    9
    − 2
    4


    =
    18 + 2
    4
    27 − 8
    4

    = 30 : 19


  1. If a : b = 5 : 7 and c : d = 2a : 3b, then ac : bd is :









  1. View Hint View Answer Discuss in Forum

    a
    =
    5
    ,
    c
    =
    2a
    b7d3b

    ⇒ 
    a
    ×
    c
    =
    5
    ×
    2a
    bd73b

    ⇒ 
    ac
    =
    10
    ×
    5
    =
    50
    bd217147

    Correct Option: B

    a
    =
    5
    ,
    c
    =
    2a
    b7d3b

    ⇒ 
    a
    ×
    c
    =
    5
    ×
    2a
    bd73b

    ⇒ 
    ac
    =
    10
    ×
    5
    =
    50
    bd217147



  1. 94 is divided into two parts in such a way that the fifth part of the first and the eighth part
    of the second are in the ratio 3 : 4. The first part is :









  1. View Hint View Answer Discuss in Forum

    First part = x and second part
    = 94 – x

    ∴  
    x

    5
    94 − x
    8

    ∴  
    x
    = 3/4
    5
    94 − x
    8

    ⇒ 
    x
    ×
    8
    =
    3
    5(94 − x)4

    ⇒  32 x = 15 × 94 – 15x
    ⇒  47 x = 15 × 94
    ⇒  x =
    15 × 94
    = 30
    47

    Correct Option: A

    First part = x and second part
    = 94 – x

    ∴  
    x

    5
    94 − x
    8

    ∴  
    x
    = 3/4
    5
    94 − x
    8

    ⇒ 
    x
    ×
    8
    =
    3
    5(94 − x)4

    ⇒  32 x = 15 × 94 – 15x
    ⇒  47 x = 15 × 94
    ⇒  x =
    15 × 94
    = 30
    47


  1. ₹ 6200 divided into three parts proportional to
    1
    :
    1
    :
    1
    235
    are respectively









  1. View Hint View Answer Discuss in Forum

    Ratio =
    1
    :
    1
    :
    1
    235

    =
    1
    × 30 :
    1
    × 30 :
    1
    × 30 = 15 : 10 : 6
    235

    Sum of the ratios
    = 15 + 10 + 6 = 31
    ∴  First part = ₹
    15
    × 6200
    31

    = ₹ 3000
    Second part = = ₹.
    10
    × 6200
    31

    = ₹ 2000
    Third part = = ₹
    6
    × 6200
    31

    = ₹ 1200

    Correct Option: A

    Ratio =
    1
    :
    1
    :
    1
    235

    =
    1
    × 30 :
    1
    × 30 :
    1
    × 30 = 15 : 10 : 6
    235

    Sum of the ratios
    = 15 + 10 + 6 = 31
    ∴  First part = ₹
    15
    × 6200
    31

    = ₹ 3000
    Second part = = ₹.
    10
    × 6200
    31

    = ₹ 2000
    Third part = = ₹
    6
    × 6200
    31

    = ₹ 1200



  1. If b is the mean proportional of a and c, then (a – b)3 : (b – c)3 equals









  1. View Hint View Answer Discuss in Forum

    Since b is the mean proportional of a and c.

    ∴ 
    a
    =
    b
    = k (Suppose)
    bc

    ∴  a = bk, b = ck
    ∴ 
    (a − b)3
    =
    (bk − b)3
    (b − c)3(ck − c)3

    =
    b3(k − 1 )3
    =
    b3
    =
    a3
    c3(k − 1 )3c3b3

    Correct Option: D

    Since b is the mean proportional of a and c.

    ∴ 
    a
    =
    b
    = k (Suppose)
    bc

    ∴  a = bk, b = ck
    ∴ 
    (a − b)3
    =
    (bk − b)3
    (b − c)3(ck − c)3

    =
    b3(k − 1 )3
    =
    b3
    =
    a3
    c3(k − 1 )3c3b3