Question

the sum of the age of a father and his son is 45years five years ago the product of their ages was 4 times the fathers age at that time find their present ages

Answer 1

f + s = 45
(f-5)(s-5)=4(f-5)
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Substitute for "f" and solve for "s":
f = 45-s
(45-s-5)(s-5) = 4(45-s-5)
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Divide both sides by 45-s-5 to get:
s-5 = 4
s = 9 (son's age now)
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Solve for "f":
f+9 = 45
f = 36 (father's age now)

Answer 2

let the father's and son's age be x and y respectively.
From the question :
x+y=45.
5yrs ago the product of their ages:
(x-5)(y-5).
it was = 4(x-5).
∴(x-5)(y-5)=4(x-5)
∴y-5=4
&y=9
we know that x+y=45.
∴x+9=45
∴x=36.
∴their present ages are:
Father:36yrs.
Son:9yrs.

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