Question

The sum of a father and his son is 45 years . 5 yrs ago , the product of their ages (in yrs)was 124 . determine their present age​

Answer 1

Let the present age of son = x

So, the present age of father = 45 - x

5 years ago,

Age of son = x - 5

and age of the father = 45 - x - 5 = 40 - x

Now, product of their ages = 124

=> (x - 5)*(40 - x) = 124

=> 40x - x2 - 5 * 40 + 5x = 124

=> 40x - x2 - 200 + 5x = 124

=> 45x - x2 - 200 = 124

=> 45x - x2 - 200 - 124 = 0

=> 45x - x2 - 324 = 0

=> x2 - 45x + 324 = 0

=> x2 - 36x - 9x + 324 = 0

=> x(x - 36) - 9(x - 36) = 0

=> (x - 36)*(x - 9) = 0

=> x = 9, 36

If the present age of son is 9 years

then present age of father = 45 - 9 = 36 years

Again, if the present age of son is 36 years

then present age of father = 45 - 36 = 9 years

which is not possible.

So, the present age of son is 9 years and the present age of the father is 36 years.

Hope This Helps you....

Have A nice day.....

Answer 2

Answer:

The present age of father = 36 years

The present age of son = 9 years.

Step-by-step explanation:

x + y = 45  ...(1)

Five years ago, the product of their ages was 124.

(x – 5) × (y – 5) = 124

⇒ (45 – y - 5) ×(y – 5) = 124  

⇒ 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

Putting y value in Eq 1

x + y = 45

x + 9 = 45

x = 45 - 9

x = 36

∴ x = 36

∴ y = 9