Question

the sum of ages of father and son is 45 . 5 years ago the product f their ages was 4 times the age of the father at that time . find the present age of father.

Answer 1

Let the age of father be x yrs
Then son`s age = (45 - x) yrs   [∵ their ages sum up to 45]
5 Years ago father`s age = (x - 5) yrs
5 years ago son`s age = (45 - x - 5) yrs = (40 - x) yrs
According to the question it is given that 
(x-5) (40-x) = 4(x-5)
⇒40x - x² - 200 + 5x = 4x - 20
⇒ 0 = -40x + x² + 200 - 5x + 4x - 20
⇒x² -45x +4x + 180 = 0
⇒x² - 41x +180 =0 
∵This equation can not be solved by factorisation we can use completing square method
⇒x² -41x +180 = 0
⇒x² -2x(41/2) + (41/2)² - (41/2)² + 180 = 0
⇒(x - 41/2)² = (1681/4) - 180 
⇒(x - 41/2)² = (1681 - 720)/4
⇒(x - 41/2)² = 961/4
⇒x - 41/2 = +/-√961/4
⇒x - 41/2 = +/-31/2
⇒x = 41/2 +/- 31/2
∴ x = 41/2 +31/2     or      x=41/2 - 31/2 
⇒x = (41 + 31)/2     or     x=(41 -31)/2
⇒x = 72/2                or     x=10/2
⇒x = 36                   or     x=5
∴ Age of the father  = 36yrs