MathematicsSix years hence a man’s age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.

Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.


  1. A
    20 years and 5 years
  2. B
    30 years and 6 years
  3. C
    10 years and 2 years
  4. D
    35 years and 11 years 

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    Solution:

    Given: After six years a man’s age will be three times the age of his son, whereas men were nine times the age of his son before three years.
    Let x be the present age of man and y be the present age of the son.
    According to first condition,
    x+6=3(y+6)   ⇒x+6=3y+18 ⇒x=3y+12    ………(1)
    According to second condition,
    x-3=9(y-3)    ……….(2)
    Substitute the value of x in (2) to find y.
    (3y+12)-3=9y-27
    ⇒3y-9y=-27-9
    ⇒-6y=-36
    ⇒y=6
    Substitute the value of y in (1) to find x.
    x=3×6+12
    ⇒x=30
    Therefore, the present age of the man and his son is 30 years and 6 years respectively.
    Hence, option 2 is correct.
     
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