Question

The sum of the ages of father and his son is 42 years. The product of their ages is 185, find their ages.

Answer 1

Let the father’s age be x years. Then, the son’s age will be (42 – x) years.
Thus, by the given condition,
x(42 – x) = 185
$\Rightarrow$ 42x – x² = 185
$\Rightarrow$ x² – 42x + 185 = 0
On splitting the middle term –42x as –5x – 37x, we get:
x² – 5x – 37x + 185 = 0
$\Rightarrow$ x(x – 5) – 37(x – 5) = 0
$\Rightarrow$ (x – 5)(x – 37) = 0
$\Rightarrow$ x – 5 = 0 or x – 37 = 0
$\Rightarrow$ x = 5 or x = 37
Since the father’s age will be greater than the son’s age, x = 37 and (42 – x) = 42 – 37 = 5.
Thus, the father’s age is 37 years and the son’s age is 5 years.