Mathematics
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
Answer
Let age of son be x years so father's age = (45 - x) years.
Five years ago age of,
son = x - 5
man = 45 - x - 5 = 40 - x
According to question,
⇒ (x - 5)(40 - x) = 124
⇒ 40x - x2 - 200 + 5x = 124
⇒ 45x - x2 - 200 - 124 = 0
⇒ x2 - 45x + 324 = 0
⇒ x2 - 36x - 9x + 324 = 0
⇒ x(x - 36) - 9(x - 36) = 0
⇒ (x - 9)(x - 36) = 0
⇒ x - 9 = 0 or x - 36 = 0
⇒ x = 9 or x = 36.
Father's age = 45 - x
Substituting x = 9 we get,
Father's age = 45 - x = 45 - 9 = 36
Substituting x = 36 we get,
Father's age = 45 - x = 45 - 36 = 9.
This is not possible as father's age cannot be less than son's age.
Hence, age of son = 9 years and that of father = 36 years.
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