Question

the sum of the age of father and son 45 year.five year ago the product of their was 4time the father age at the time .the present age of the father on respectively are?​

Answer 1

Step-by-step explanation:

Let the present age of father and son be x and y

According to question:

x + y = 45 ...(1)

5 years ago, the product of their ages was 124, therefore,

(x – 5) × (y – 5) = 124

$\sf \: ⇒ (45 – y - 5) ×(y – 5) = 124 [using Eq -1] \\ \sf⇒ 40y – y^2 - 200 + 5y = 124 \\ \sf⇒ y^2 - 45y + 324 = 0 \\ \sf⇒ y^2 - 36y - 9y + 324 = 0 \\ \sf⇒ y(y - 36) -9 (y - 36) = 0 \\ \sf⇒ (y - 36)(y - 9) = 0 \\ \sf⇒ y = 36 or y = 9$

For y = 36, x = 45 - 36 = 9 which is not possible.

For y = 9, x = 45 - 9 = 36

$\sf Therefore \: the \: present \: age \: of \: father \: = 36 years \: \\ \sf and \: the \: present \: age \: of \: son \: = 9 \: years.$