Ratio, Proportion


  1. Of three positive numbers, the ratio of 1st and 2nd is 8 : 9, that of 2nd and 3rd is 3:4. The product of 1st and 3rd is 2400. The sum of the three numbers is









  1. View Hint View Answer Discuss in Forum

    A : B = 8 : 9
    B : C = 3 : 4 = 9 : 12
    ∴  A : B : C = 8 : 9 : 12
    ∴  Numbers = 8x, 9x and 12x
    ∴  8x × 12x = 2400

    ⇒  x2 =
    2400
    = 25
    8 × 12

    ∴  x = √25 = 5
    ∴  A + B + C = 8x + 9x + 12x
    = 29x
    = 29 × 5 = 145

    Correct Option: A

    A : B = 8 : 9
    B : C = 3 : 4 = 9 : 12
    ∴  A : B : C = 8 : 9 : 12
    ∴  Numbers = 8x, 9x and 12x
    ∴  8x × 12x = 2400

    ⇒  x2 =
    2400
    = 25
    8 × 12

    ∴  x = √25 = 5
    ∴  A + B + C = 8x + 9x + 12x
    = 29x
    = 29 × 5 = 145


  1. What number should be added to each of 6, 14, 18 and 38 so that the resulting numbers make a proportion ?









  1. View Hint View Answer Discuss in Forum

    6 + x
    =
    18 + x
    14 + x38 + x

    From the given alternatives
    6 + 2
    =
    18 + 2
    14 + 238 + 2

    ⇒ 
    1
    =
    1
    2 2

    Second Method :
    Here, a = 6, b = 14, c = 18, d = 38
    Required number x =
    bc − ad
    (a + d) − (b + c)

    =
    14 × 18 − 6 × 38
    (6 + 38) − (14 + 18)

    =
    252 − 228
    44 − 32

    =
    24
    = 2
    12

    Correct Option: B

    6 + x
    =
    18 + x
    14 + x38 + x

    From the given alternatives
    6 + 2
    =
    18 + 2
    14 + 238 + 2

    ⇒ 
    1
    =
    1
    2 2

    Second Method :
    Here, a = 6, b = 14, c = 18, d = 38
    Required number x =
    bc − ad
    (a + d) − (b + c)

    =
    14 × 18 − 6 × 38
    (6 + 38) − (14 + 18)

    =
    252 − 228
    44 − 32

    =
    24
    = 2
    12



  1. Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional ?









  1. View Hint View Answer Discuss in Forum

    Let required number be x.

    ∴ 
    6 + x
    =
    15 + x
    7 + x17 + x

    ⇒  102 + 17x + 6x + x2
    = 105 + 7x + 15x + x2
    ⇒  23x – 22x = 105 – 102
    ⇒  x = 3
    Note : It is convenient to solve it orally using options
    6 + 3
    =
    15 + 3
    9
    =
    18
    7 + 317 + 3 1020

    Second Method :
    Required Number =
    bc − ad
    (a + d) − (b + c)

    Where a = 6, b = 7, c = 15, d = 17
    =
    7 × 15 − 6 × 17
    (6 + 17) − (7 + 15)

    =
    105 − 102
    = 3
    23 − 22

    Correct Option: D

    Let required number be x.

    ∴ 
    6 + x
    =
    15 + x
    7 + x17 + x

    ⇒  102 + 17x + 6x + x2
    = 105 + 7x + 15x + x2
    ⇒  23x – 22x = 105 – 102
    ⇒  x = 3
    Note : It is convenient to solve it orally using options
    6 + 3
    =
    15 + 3
    9
    =
    18
    7 + 317 + 3 1020

    Second Method :
    Required Number =
    bc − ad
    (a + d) − (b + c)

    Where a = 6, b = 7, c = 15, d = 17
    =
    7 × 15 − 6 × 17
    (6 + 17) − (7 + 15)

    =
    105 − 102
    = 3
    23 − 22


  1. Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be 3x, 4x and 5x.
    ∴  5x + 3x = 4x + 52
    ⇒  4x = 52 ⇒ x =13
    ∴  The smallest number
    = 3x = 3 × 13 = 39

    Correct Option: C

    Let the numbers be 3x, 4x and 5x.
    ∴  5x + 3x = 4x + 52
    ⇒  4x = 52 ⇒ x =13
    ∴  The smallest number
    = 3x = 3 × 13 = 39



  1. If the sum of two quantities is equal to three times their difference, then the ratio of the two
    quantities is









  1. View Hint View Answer Discuss in Forum

    x + y = 3 (x – y)
    ⇒  x + y = 3x – 3y Þ 2x = 4y

    ⇒ 
    x
    =
    2
    ⇒ x : y = 2 : 1
    y1

    Correct Option: C

    x + y = 3 (x – y)
    ⇒  x + y = 3x – 3y Þ 2x = 4y

    ⇒ 
    x
    =
    2
    ⇒ x : y = 2 : 1
    y1