Question

The sum of ages of a father and his son is 45 years.5 years ago,the rpoduct of their ages(in years) was 124.Determine the present ages of father and his son respectively.

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

Ans : Present age of father : 36 years

        Present age of son : 9 years

#hope it helps