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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.
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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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