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प्रश्न
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.
उत्तर
Let the present ages of father and his son be x years and (45 – x) years respectively.
Five years ago,
Father's age = (x – 5) years
Son's age = (45 – x – 5) years = (40 – x) years
From the given information, we have:
(x – 5)(40 – x) = 124
40x – x2 – 200 + 5x = 124
x2 – 45x + 324 = 0
x2 – 36x – 9x + 324 = 0
x(x – 36) – 9(x – 36) = 0
(x – 36)(x – 9) = 0
x = 36, 9
if x = 9,
Father's age = 9 years,
Son's age = (45 – x) = 36 years
This is not possible.
Hence, x = 36
Father's age = 36 years
Son's age = (45 – 36) years = 9 years.
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