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Question
A boy is now one-third as old as his father. Twelve years hence he will be half as old as his father. Determine the present ages of the boy and that of his father.
Solution
Given, present age of boy is one-third as that of his father.
So, let the present age of the son be x years.
Then, present age of father is 3x years.
Twelve years hence, their ages becomes, (x + 12) and (3x + 12) respectively.
As per given conditions,
`((x + 12))/((3x + 12)) = (1)/(2)`
⇒ 2x + 24 = 3x + 12
⇒ x = 12 years
Thus, the present age of the son is 12 years.
Then, present age of father is 36 years.
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