The sum of ages of a father and his son is 45 years. Five years ago, the product of their age was 124. Determine their present ages.

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Solution

Let father's present age be $x$ years.

Son's present age $= 45 - x$

Therefore,

$\Rightarrow$ $(x - 5) (40 - x) = 124$

$\Rightarrow$ $40 x - x^{2} - 200 + 5 x = 124$

$\Rightarrow$ $x^{2} - 45 x + 324 = 0$

$\Rightarrow$ $(x - 9) (x - 36) = 0$

$\Rightarrow$ $x = 9, 36$

Clearly $x$ cannot be $9$

Therefore,

Father's present age = $x = 36$ years

Son's present age = $45 - 36 = 9$ years

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The sum of ages of a father and his son is 45 years. Five years ago, the product of their age was 124. Determine their present ages.

Let father's present age be x years.Son's present age =45−xTherefore,⇒(x−5)(40−x)=124⇒40x−x2−200+5x=124⇒x2−45x+324=0⇒(x−9)(x−36)=0⇒x=9,36Clearly x cannot be 9Therefore,Father's present age = x=36 yearsSon's present age = 45−36=9 years