Ratio, Proportion


  1. There are three numbers A, B, C such that twice A is equal to thrice B and four times B is equal to five times C. Then the ratio between A and C is









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    As given,
    2A = 3B
    ⇒  A : B = 3 : 2
    and, 4B = 5C
    ⇒  B : C = 5 : 4
    ∴  A : B : C
    = 3 × 5 : 2 × 5 : 2 × 4
    = 15 : 10 : 8
    ∴  A : C = 15 : 8
    Second Method :
    Here, 2A = 3B i,eA : B = 3 : 2
    4B = 5C i,e B : C = 5 : 4
    A : C = xp : yq
    = 3 × 5 : 2 × 4
    = 15 : 8

    Correct Option: C

    As given,
    2A = 3B
    ⇒  A : B = 3 : 2
    and, 4B = 5C
    ⇒  B : C = 5 : 4
    ∴  A : B : C
    = 3 × 5 : 2 × 5 : 2 × 4
    = 15 : 10 : 8
    ∴  A : C = 15 : 8
    Second Method :
    Here, 2A = 3B i,eA : B = 3 : 2
    4B = 5C i,e B : C = 5 : 4
    A : C = xp : yq
    = 3 × 5 : 2 × 4
    = 15 : 8


  1. If x : y = 3 : 4, then the value of
    5x − 2y
    =
    7x + 2y









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    x
    =
    3
    (Given)
    y4

    ∴ 
    5x − 2y
    7x + 2y

    = 5
    x
    − 2
    y
    7
    x
    + 2
    y

    = 5 ×
    3
    − 2
    4
    7 ×
    3
    + 2
    4

    =
    15 − 8
    4
    21 + 8
    4

    =
    7
    29

    Correct Option: C

    x
    =
    3
    (Given)
    y4

    ∴ 
    5x − 2y
    7x + 2y

    = 5
    x
    − 2
    y
    7
    x
    + 2
    y

    = 5 ×
    3
    − 2
    4
    7 ×
    3
    + 2
    4

    =
    15 − 8
    4
    21 + 8
    4

    =
    7
    29



  1. The third proportional to 0.8 and 0.2 is :









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    If the third proportional be x,then
    0.8 : 0.2 : : 0.2 : x
    ⇒  0.8 × x = 0.2 × 0.2

    ⇒ x =
    0.2 × 0.2
    0.8

    =
    4
    = 0.05
    80

    Second Method :
    Third proportion
    =
    b2
    =
    (0.2)2
    a0.8

    =
    0.04
    = 0.05
    0.8

    Correct Option: A

    If the third proportional be x,then
    0.8 : 0.2 : : 0.2 : x
    ⇒  0.8 × x = 0.2 × 0.2

    ⇒ x =
    0.2 × 0.2
    0.8

    =
    4
    = 0.05
    80

    Second Method :
    Third proportion
    =
    b2
    =
    (0.2)2
    a0.8

    =
    0.04
    = 0.05
    0.8


  1. If A : B = 4 : 9 and A : C = 2 : 3, then (A + B) : (A + C) is









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    A : B = 4 : 9
    A : C = 2 : 3 = 4 : 6

    ∴ 
    A + B
    =
    4 + 9
    =
    13
    A + C4 + 610

    Correct Option: C

    A : B = 4 : 9
    A : C = 2 : 3 = 4 : 6

    ∴ 
    A + B
    =
    4 + 9
    =
    13
    A + C4 + 610



  1. Marks of two candidates P and Q are in the ratio of 2 : 5. If the marks of P is 120, marks of Q will be









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    Marks of Q =
    5
    × 120 = 300
    2

    Correct Option: C

    Marks of Q =
    5
    × 120 = 300
    2