the sum of ages of a father and son is 45 years five years ago the products of their. ages was 4 times the ages of the fathervat that time the present age of the father
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Let the present age of father = x years and the present age of son = y years
According to question:
x + y = 45 ...(1)
Again, 5 years ago, the product of their ages was 124, therefore,
(Age of man 5 years ago) × (Age of son 5 years ago) = 124
(x – 5) × (y – 5) = 124
⇒ (45 – y - 5) ×(y – 5) = 124 [Using (1)]
⇒ 40y – y2 - 200 + 5y = 124
⇒ y2 - 45y + 324 = 0
⇒ y2 - 36y - 9y + 324 = 0
⇒ y(y - 36) -9 (y - 36) = 0
⇒ (y - 36)(y - 9) = 0
⇒ y = 36 or y = 9
For y = 36, x = 45 - 36 = 9 which is not possible.
For y = 9, x = 45 - 9 = 36
Therefore, the present age of father = 36 years and the present age of son = 9 years.
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