The sum of the ages of father and his son is 45 years . 5 years ago the products of their ages was 124. Find the present ages .

Explanation

Let the present age of the man be x years.
Then, the present age of the son `=(45-x)` years.
Age of the man 5 years ago `=(x-5)` years.
Age of the son 5 years ago `=(45-x-5)` years `=(40-x)` years.
`:." "(x-5)(40-x)=124`
`implies" "-x^(2)+45x-200=124impliesx^(2)-45x+324=0`
`implies" "x^(2)-36x-9x+324=0impliesx(x-36)-9(x-36)=0`
`implies" "(x-36)(x-9)=0impliesx-36=0" or "x-9=0`
`implies" "x=36" or "x=9.`
But, the man's age cannot be 9 years. So we reject x=9.
Hence, the man's present age = 36 years.
And, the son's present age `=(45-36)` years=9 years.