Question

The sum of ages(in years) of a son and his father is 35years and product of their ages is 150 years ,find their ages.

Answer 1

If we find mif we find the factors of 150

Factors of 150 are 1,2,3,5,10,15,25,75,150

then sum two factor should be 35

10+25=30

therefore age of sin = 10

and father = 25

Answer 2

Given that

Sum of the ages of son and father = 35 yrs

Product of ages of son and father = 150 year

Now let the age of children be x then age of father = (35-x)

Now also given that

father's age × children age = 150

=>( 35-x) ×( x) = 150

=> 35x - x² = 150

or

x² - 35x + 150 = 0

now by factorising

= x² - 30x - 5x + 150

= x(x-30) - 5(x-30)

= (x-30)(x-5)

then possible values of x = 5 & 30

But as son can not be elder than his father

therefore x = 5 is only the solution

Then

age of son = 5 years

age of father = 30 years