Ratio, Proportion


  1. If x : y = 3 : 1, then x3 – y3 : x3 + y3 = ?









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    x
    =
    3
    x3
    =
    27
    y1y31

    ⇒ 
    x3 − y3
    =
    27 − 1
    x3 − y327 + 1

    [By componendo and dividendo]
    =
    26
    =
    13
    = 13 : 14
    2814

    Correct Option: A

    x
    =
    3
    x3
    =
    27
    y1y31

    ⇒ 
    x3 − y3
    =
    27 − 1
    x3 − y327 + 1

    [By componendo and dividendo]
    =
    26
    =
    13
    = 13 : 14
    2814


  1. If a : b = c : d = e : f = 1 : 2, then (pa + qc + re) : (pb + qd + rf) is equal to :









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    a
    =
    c
    =
    e
    =
    1
    bdf2

    ⇒ 
    pa
    =
    qc
    =
    re
    =
    1
    pbqdrf2

    ⇒ 
    pa + qc + re
    =
    1
      or   1 : 2
    pb + qd + rf2

    Correct Option: D

    a
    =
    c
    =
    e
    =
    1
    bdf2

    ⇒ 
    pa
    =
    qc
    =
    re
    =
    1
    pbqdrf2

    ⇒ 
    pa + qc + re
    =
    1
      or   1 : 2
    pb + qd + rf2



  1. If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns +ou) is equal to :









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    If
    a
    =
    c
    =
    e
    , then each of
    bdf

    these ratios is equal to
    a + c + e
    b + d + f

    Here,
    p
    =
    r
    =
    t
    =
    2
    qsu3

    ⇒ 
    mp
    =
    nr
    =
    ot
    =
    2
    mqnsou3

    ⇒ 
    mp + nr + ot
    :
    2
      or   2 : 3
    mq + ns + ou3

    Correct Option: C

    If
    a
    =
    c
    =
    e
    , then each of
    bdf

    these ratios is equal to
    a + c + e
    b + d + f

    Here,
    p
    =
    r
    =
    t
    =
    2
    qsu3

    ⇒ 
    mp
    =
    nr
    =
    ot
    =
    2
    mqnsou3

    ⇒ 
    mp + nr + ot
    :
    2
      or   2 : 3
    mq + ns + ou3


  1. If   x =
    1
    y and y =
    1
    z
    32
    then x : y : z, is equal to :









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    x =
    1
    y ⇒ x : y = 1 : 3
    3
    Again, y =
    1
    z ⇒ y : z
    2

    = 1 : 2 = 3 : 6
    ∴  x : y : z = 1 : 3 : 6

    Correct Option: C

    x =
    1
    y ⇒ x : y = 1 : 3
    3
    Again, y =
    1
    z ⇒ y : z
    2

    = 1 : 2 = 3 : 6
    ∴  x : y : z = 1 : 3 : 6



  1. If a : b = 7 : 9 and b : c =15 : 7, then what is a : c?









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    a : c = (a : b) × (b : c)

    =
    7
    ×
    15
    =
    15
    = 5 : 3
    979

    Second Method :
    A : C = 7 × 15 : 9 × 7 = 5 : 3

    Correct Option: A

    a : c = (a : b) × (b : c)

    =
    7
    ×
    15
    =
    15
    = 5 : 3
    979

    Second Method :
    A : C = 7 × 15 : 9 × 7 = 5 : 3