Ratio, Proportion


  1. If a : (b+c) = 1 : 3 and c : (a+ b) = 5:7, then b : (a+c) is equal to









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    a : (b+c) = 1: 3

    ⇒ 
    b + c
    =
    3
    b + c
    + 1 =
    3
    + 1
    a1a1

    ⇒ 
    a + b + c
    =
    3 + 1
    =
    4
       ..... (i)
    a11

    Similarly,
    a + b
    =
    7
    c5

    ⇒ 
    a + b + c
    =
    12
        ..... (ii)
    c5

    On dividing (i) by (ii),
    c
    =
    4 × 5
    =
    5
    = k    ..... (iii)
    a123

    From equation (i), b = 4k
    ∴  
    b
    =
    4k
    = 1: 2
    a + c3k + 5k

    Correct Option: A

    a : (b+c) = 1: 3

    ⇒ 
    b + c
    =
    3
    b + c
    + 1 =
    3
    + 1
    a1a1

    ⇒ 
    a + b + c
    =
    3 + 1
    =
    4
       ..... (i)
    a11

    Similarly,
    a + b
    =
    7
    c5

    ⇒ 
    a + b + c
    =
    12
        ..... (ii)
    c5

    On dividing (i) by (ii),
    c
    =
    4 × 5
    =
    5
    = k    ..... (iii)
    a123

    From equation (i), b = 4k
    ∴  
    b
    =
    4k
    = 1: 2
    a + c3k + 5k


  1. If a : b = c : d = e : f = 1 : 2, then ( 3a + 5c +7e): (3b + 5d + 7 f ) is equal to









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    a
    =
    c
    =
    e
    =
    1
    bdf2
    ∴ 
    3a
    =
    5c
    =
    7e
    =
    1
    3b5d7f2

    ∴  
    3a + 5c + 7e
    =
    1
    = 1 : 2
    3b + 5d + 7f2

    Correct Option: D

    a
    =
    c
    =
    e
    =
    1
    bdf2
    ∴ 
    3a
    =
    5c
    =
    7e
    =
    1
    3b5d7f2

    ∴  
    3a + 5c + 7e
    =
    1
    = 1 : 2
    3b + 5d + 7f2



  1. If A : B : C = 2 : 3 : 4, then ratio
    A
    :
    B
    :
    C
    is equal to
    BCA









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    A : B : C = 2 : 3 : 4

    ∴  
    A
    =
    2
    ,
    B
    =
    3
    ,
    C
    =
    4
    = 2
    B3C4A2

    ∴  
    A
    :
    B
    :
    C
    =
    2
    :
    3
    :
    2
    BCA341

    = 8 : 9 : 24

    Correct Option: C

    A : B : C = 2 : 3 : 4

    ∴  
    A
    =
    2
    ,
    B
    =
    3
    ,
    C
    =
    4
    = 2
    B3C4A2

    ∴  
    A
    :
    B
    :
    C
    =
    2
    :
    3
    :
    2
    BCA341

    = 8 : 9 : 24


  1. If   A : B =
    1
    :
    3
    , B : C =
    1
    :
    5
    2839
    and C : D =
    5
    :
    3
    then the ratio A : B : C : D is
    64









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    A : B =
    1
    :
    3
    = 4 : 3 = 8 : 6
    28

    B : C =
    1
    :
    5
    = 3 : 5 = 6 : 10
    39

    C : D =
    5
    :
    3
    = 10 : 9
    64

    ∴  A : B : C : D = 8 : 6 : 10 : 9

    Correct Option: C

    A : B =
    1
    :
    3
    = 4 : 3 = 8 : 6
    28

    B : C =
    1
    :
    5
    = 3 : 5 = 6 : 10
    39

    C : D =
    5
    :
    3
    = 10 : 9
    64

    ∴  A : B : C : D = 8 : 6 : 10 : 9



  1. If a : b = b : c, then a4 : b4 is equal to









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    a
    =
    b
    bc

    ⇒  b2 = ac ⇒ b4 = a2c2
    ∴ 
    a4
    =
    a4
    =
    a2
    b4a2c2c2

    Correct Option: B

    a
    =
    b
    bc

    ⇒  b2 = ac ⇒ b4 = a2c2
    ∴ 
    a4
    =
    a4
    =
    a2
    b4a2c2c2