Ratio, Proportion


  1. Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?









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    Let x years ago the ratio of their age was 3 : 5
    ∴  According to the question

    40 − x
    =
    3
    60 − x5

    ⇒  200 – 5x = 180 – 3x
    ⇒  2x = 20
    ∴  x = 10 years

    Correct Option: A

    Let x years ago the ratio of their age was 3 : 5
    ∴  According to the question

    40 − x
    =
    3
    60 − x5

    ⇒  200 – 5x = 180 – 3x
    ⇒  2x = 20
    ∴  x = 10 years


  1. The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be









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    Sumit’s present age = 2x years
    Prakash’s present age = 3x years
    ∴  3x– 2x = 6
    x = 6
    ∴  Required ratio
    = (2 × 6 + 6) : (3 × 6 + 6)
    = 18 : 24 = 3 : 4

    Correct Option: D

    Sumit’s present age = 2x years
    Prakash’s present age = 3x years
    ∴  3x– 2x = 6
    x = 6
    ∴  Required ratio
    = (2 × 6 + 6) : (3 × 6 + 6)
    = 18 : 24 = 3 : 4



  1. The ratio of the age of a father to that of his son is 5: 2. If the product of their ages in years is 1000, then the father's age (in years) after 10 years will be :









  1. View Hint View Answer Discuss in Forum

    Let father’s age be 5x years.
    Son’s age = 2x years
    ∴  5x × 2x = 1000
    ⇒  x2 = 100 ⇒ x = 10
    ∴  Father’s age after 10 years
    = 5x + 10
    = 5 × 10 + 10 = 60 years

    Correct Option: B

    Let father’s age be 5x years.
    Son’s age = 2x years
    ∴  5x × 2x = 1000
    ⇒  x2 = 100 ⇒ x = 10
    ∴  Father’s age after 10 years
    = 5x + 10
    = 5 × 10 + 10 = 60 years


  1. The ratio of the age of Ram and Rahim 10 years ago was 1 : 3. The ratio of their age five years hence will be 2 : 3. Then the ratio of their present age is









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    Let the age of Ram and Rahim 10 years ago be x and 3x years respectively.
    After 5 years from now,

    x + 15
    =
    2
    3x + 153

    ⇒  6x + 30 = 3x + 45
    ⇒  3x = 45 – 30 = 15
    ∴  Ratio of their present age
    = (x + 10) : (3x + 10)
    = 15 : 25 = 3 : 5

    Correct Option: B

    Let the age of Ram and Rahim 10 years ago be x and 3x years respectively.
    After 5 years from now,

    x + 15
    =
    2
    3x + 153

    ⇒  6x + 30 = 3x + 45
    ⇒  3x = 45 – 30 = 15
    ∴  Ratio of their present age
    = (x + 10) : (3x + 10)
    = 15 : 25 = 3 : 5



  1. At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is









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    Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.
    After 15 years,

    6x + 15
    =
    9
    5x + 158

    ⇒  48x + 120 = 45x + 135
    ⇒  48x – 45x = 135 – 120
    ⇒  3x = 15 ⇒ x = 5
    ∴  Maya’s present age = 6x
    = 6 × 5 = 30 years

    Correct Option: C

    Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.
    After 15 years,

    6x + 15
    =
    9
    5x + 158

    ⇒  48x + 120 = 45x + 135
    ⇒  48x – 45x = 135 – 120
    ⇒  3x = 15 ⇒ x = 5
    ∴  Maya’s present age = 6x
    = 6 × 5 = 30 years