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

EXPLANATION.

Sum of age of father and son be = 45 years.

Let, the age of father be = x.

Then, age of son be = 45 - x.

Five years ago,

Now, the age of father be = (x - 5).

Now, the age of son be = [(45 - x) - 5] = (40 - x).

The products of their age was four times the father age at that time,

⇒ (x - 5)(40 - x) = 4(x - 5).

⇒ 40x - x² - 200 + 5x = 4x - 20.

⇒ 45x - x² - 200 = 4x - 20.

⇒ 4x - 20 + x² - 45x + 200 = 0.

⇒ x² - 41x + 180 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² - 36x - 5x + 180 = 0.

⇒ x(x - 36) - 5(x - 36) = 0.

⇒ (x - 5)(x - 36) = 0.

⇒ x = 5  and  x = 36.

Considered, x = 36.

Now, the present age of father be = x = 36 years.

Present age of son be = 45 - 36 = 9 years.

Answer 2

Step-by-step explanation:

$\sf \: Let \: the \: present \: age \: of \: father \: = x years \\ \sf \: and \: the \: present \: age \: of son \: = y \:  years$

$\bold \purple{according \: to \: the \: question}$

$\sf \: x + y = 45 ...(1)$

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

(Age of man 5 years ago) × (Age of son 5 years ago) = 124

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

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

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

Therefore, the present age of father = 36 years and the present age of son = 9 years.