The sum of ages of a father & his son is45. 5 years ago, the product of their ages was 124. Determine their present age.

present age

let age of son be x

let age of father be y

x + y = 45

y = 45 - x

so age of father can also be taken as y = 45 - x

age after 5 years

father's age = y + 5 = 45 - x + 5 = 50 -x

son's age = x + 5

( x + 5 ) ( 50 - x ) = 124

45x - x² + 250  = 124

45x - x² - 76 = 0

-x² + 45x - 126 = 0

dividing the equation by -1 to make x² positive

x²  - 45x + 126 = 0

sum = -45, product = 126

x² - 3x - 42x + 126 = 0

x ( x - 3 ) -42 ( x - 3 ) = 0

( x - 3 ) ( x - 42 ) = 0

x = 3, 42

age of son = x = 3

age of father = y = 45 - x = 45 - 3 = 42