Calculate the Present Age of Father and Son
The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son?
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Let us assume, The present age of Father is x years and present age of Son is y years.
Given:
x + y = 45
y = 45 - x------------1
Also given:
Five years ago,
(x - 5) (y -5) = 4 (x - 5)
xy - 5x - 5y + 25 = 4x - 20
xy - 5y - 9x = - 45
9x - xy + 5y = 45 ----------2
Substitute the value of x from equation 1 in equation 2
9x - x (45 - x) + 5 ( 45 - x) = 45
9x - 45x + x + 225 - 5x = 45
x^2 - 41x + 180 = 0
Solve the quadaratic equation to find out the roots, by using the formula
x = (-b +/- sqrt (b^2 - 4ac))/2a
You will get x = 36 and x = 5
Father's age is not very less, so consider it as x = 36 years.
Therefore, Son's age is 45 - x = 45 - 36 = 9 years
Given:
x + y = 45
y = 45 - x------------1
Also given:
Five years ago,
(x - 5) (y -5) = 4 (x - 5)
xy - 5x - 5y + 25 = 4x - 20
xy - 5y - 9x = - 45
9x - xy + 5y = 45 ----------2
Substitute the value of x from equation 1 in equation 2
9x - x (45 - x) + 5 ( 45 - x) = 45
9x - 45x + x + 225 - 5x = 45
x^2 - 41x + 180 = 0
Solve the quadaratic equation to find out the roots, by using the formula
x = (-b +/- sqrt (b^2 - 4ac))/2a
You will get x = 36 and x = 5
Father's age is not very less, so consider it as x = 36 years.
Therefore, Son's age is 45 - x = 45 - 36 = 9 years
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