# 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.

1
by rollypolly

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by rollypolly

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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