Question

the sum of the ages of a father and a son is 45 years. Five years ago, the product of their ages was 34. The ages of father and son are
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Answer 1

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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Answer 2

Let sons age = x years. Then fathers age = (45 - x)years.
(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9
Their ages are 36 years and 9 years


this is a easy way to solve