Ratio, Proportion


  1. In a 45 litres mixture of milk and water, the ratio of the milk to water is 2 : 1. When some quantity of water is added to the mixture, this ratio becomes 1 : 2. The quantity of water added is









  1. View Hint View Answer Discuss in Forum

    Quantity of milk in 45 litres =
    2
    × 45 = 30 litres.
    3

    ∴  Water = (45 – 15)
    = 15 litres
    Let x litres of water be added.
    ∴ 
    30
    =
    1
    15 + x2

    ⇒  15 + x = 60
    ⇒  x = 60 – 15 = 45 litres.

    Correct Option: D

    Quantity of milk in 45 litres =
    2
    × 45 = 30 litres.
    3

    ∴  Water = (45 – 15)
    = 15 litres
    Let x litres of water be added.
    ∴ 
    30
    =
    1
    15 + x2

    ⇒  15 + x = 60
    ⇒  x = 60 – 15 = 45 litres.


  1. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x, y and z. Then
    x : y = 2 : 3 ; y : z = 5 : 8
    ∴  x : y : z = 2 × 5 : 3 × 5 : 3 × 8
    = 10 : 15 : 24
    Sum of the ratios
    = 10 + 15 + 24 = 49

    ∴  The second number =
    15
    × 45 = 30
    49

    Correct Option: C

    Let the numbers be x, y and z. Then
    x : y = 2 : 3 ; y : z = 5 : 8
    ∴  x : y : z = 2 × 5 : 3 × 5 : 3 × 8
    = 10 : 15 : 24
    Sum of the ratios
    = 10 + 15 + 24 = 49

    ∴  The second number =
    15
    × 45 = 30
    49



  1. The sum of three numbers is 116. The ratio of second to the third is 9 : 16 and the first to
    the third is 1 : 4. The second number is









  1. View Hint View Answer Discuss in Forum


    Therefore, second number

    =
    9
    × 116 =
    9
    × 116
    9 + 16 + 429

    = 36

    Correct Option: D


    Therefore, second number

    =
    9
    × 116 =
    9
    × 116
    9 + 16 + 429

    = 36


  1. Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be 3x, 2x
    and 5x respectively.
    Now,  (3x)2 + (2x)2 + (5x)2
    = 1862
    ⇒  9x2 + 4x2 + 25x2 = 1862
    ⇒  38x2 = 1862

    ⇒  x2 =
    1862
    = 49
    38

    ⇒  x = √49 = 7
    ∴  The smallest number
    = 2x = 2 × 7 = 14

    Correct Option: C

    Let the numbers be 3x, 2x
    and 5x respectively.
    Now,  (3x)2 + (2x)2 + (5x)2
    = 1862
    ⇒  9x2 + 4x2 + 25x2 = 1862
    ⇒  38x2 = 1862

    ⇒  x2 =
    1862
    = 49
    38

    ⇒  x = √49 = 7
    ∴  The smallest number
    = 2x = 2 × 7 = 14



  1. The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is









  1. View Hint View Answer Discuss in Forum

    Let the integers be 9x and 7x respectively.
    According to the question,
    9x × 7x = 1575

    ⇒  x2 =
    1575
    63

    ⇒  x2 = 25
    ⇒  x = 5
    [x being positive (+ve) integer]
    ∴  Smaller integer
    = 7x = 7 × 5 = 35

    Correct Option: B

    Let the integers be 9x and 7x respectively.
    According to the question,
    9x × 7x = 1575

    ⇒  x2 =
    1575
    63

    ⇒  x2 = 25
    ⇒  x = 5
    [x being positive (+ve) integer]
    ∴  Smaller integer
    = 7x = 7 × 5 = 35