Question

The sum of the ages of the father and the son is 45 years..five years ago,the product of their age was 124 yrs l.. determine their present ages

Answer 1

let father age be y and son age be x
therefore x+y=45
therefore
(x-5)(y-5)=124
x+y=45
x=45-y
putting the value of x into:(x-5)(y-5)=124
(45-y-5)×(y-5)=124
(40-y)×(y-5)=124
40y-200-y^2+5y=124
-y^2+45y-200=124
-y^2+45y-324=0
-y^2+36y+9y-324
-y (y-36)+9 (y-36)
therefore y=36
therefore his father age will be 36
and his son age will be x=45-y
x=9

Answer 2

Hey sup,

As per the question,

Let the age of son be x years.
So father's age = 45-x years.
Son's age < father's age.
Five years ago,
Son's age=x-5.
Father's age=45-x-5=40-x.

So,
(x-5)(40-x)=124.
=>40x-x^2-200+5x=124.
=>-x^2+45x-200-124=0.

=>-x^2+45x-324=0.
=>-x^2+36x+9x-324=0.
=>-x(x-36)+9(x-36)=0.
=>(x-36)(9-x)=0.
We'll discard (x-36) as we assumed son's age cannot be more than father's .

x-9=0.
=>x=9.

So, son's age=9 years.
Father's age=45-x=45-9=36 years.

Hope it helps.