Question

The sum of present ages of a man and his son is 45 years. 5 years ago product of their ages was 4 times that of age of man. Find their present ages.
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Answer 1

Step-by-step explanation:

Let the present age of the man be x years

Then present age of his son is (45 - x) years

Five years ago, man's age = (x - 5) years

And his son's age (45 - x - 5) = (40 - x) years

Then according to question,

(x - 5)(40 - x) = 4(x - 5)

40x - x2 + 5x - 200 = 4x - 20

-x2 + 45x - 200 = 4x - 20

-x2 + 45x - 200 - 4x + 20 = 0

-x2 + 41x - 180 = 0

x2 - 41x + 180 = 0

x2 - 36x - 5x + 180 0

x(x - 36) -5(x - 36) = 0

(x- 36)(x - 5) = 0 =

So, either

x-36 = 0

x = 36

Or

X-5 = 0

x = 5

But, the father's age never be 5 years Therefore, when x = 36 then

45 - x = 45 - 36 = 9

Hence, man's present age is36 years and his son's age is 9 years.