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Question
Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.
Solution
Five years ago:
Let the age of the son be x years .
Therefore, the age of the father will be 7x years .
∴ Present age of the son = (x + 5) years
Present age of the father = (7x + 5) years
After five years:
Age of the son = (x + 5 + 5) = (x + 10) years
Age of the father = (7x + 5 + 5) = (7x + 10) years
According to the question,
7x + 10 = 3(x + 10)
or 7x - 3x = 30 - 10
or 4x = 20
or x = 5
∴ Present age of the son = (5 + 5) = 10 years . \]
Present age of the father =\[ (7 \times 5 + 5) = 40\text{ years }.\]
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