Question:
The sum of the Ages of father and his son is 45 years .Five years ago the product of their ages (in years was 124 .Determine thier present ages
Answer:
Let the present age of son = x
So, the present age of father = 45 - x
5 years ago,
Age of son = x - 5
and age of the father = 45 - x - 5 = 40 - x
Now, product of their ages = 124
=> (x - 5)*(40 - x) = 124
=> 40x - x2 - 5 * 40 + 5x = 124
=> 40x - x2 - 200 + 5x = 124
=> 45x - x2 - 200 = 124
=> 45x - x2 - 200 - 124 = 0
=> 45x - x2 - 324 = 0
=> x2 - 45x + 324 = 0
=> x2 - 36x - 9x + 324 = 0
=> x(x - 36) - 9(x - 36) = 0
=> (x - 36)*(x - 9) = 0
=> x = 9, 36
If the present age of son is 9 years
then present age of father = 45 - 9 = 36 years
Again, if the present age of son is 36 years
then present age of father = 45 - 36 = 9 years
which is not possible.
So, the present age of son is 9 years and the present age of the father is 36 years.
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