Mathematics10 years ago the age of the father was 5 times that of the son. 20 years hence the age of the father will be twice that of the son. What is the present age of the father?

10 years ago the age of the father was 5 times that of the son. 20 years hence the age of the father will be twice that of the son. What is the present age of the father?


  1. A
    40
  2. B
    45
  3. C
    60
  4. D
    70  

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    Solution:

    Given, 10 years ago the age of the father was 5 times that of the son.
    20 years hence the age of the father will be twice that of the son.
    Let the present age of father be x years and that of son be y years.
    ⇒ x-10=5(y-10) ⇒ x-5y=-40  ...(1)
    20 years hence, the age of the father will be twice that of the son.
    ⇒ x+20=2(y+20) ⇒ x-2y=20...(2)
    Subtracting equation (1) from equation (2), we get,
    ⇒ x-x-2y+5y=20+40
    ⇒ 3y=60
    ⇒ y=20 
    Put in (1),
    ⇒ x-5(20)=-40
    ⇒ x=100-40
    ⇒ x=60.
    Therefore, the present age of father is 60 years.
    Hence, the correct option is 3.
     
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