Ashu is x years old while his mother Mrs Veena is $x^{2}$ years old. Five years hence Mrs Veena will be three times old as Ashu. The product of their present ages is:

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Solution

$\Rightarrow$ Ashu's age $= x y e a r s$
$\Rightarrow$ Ashu's mother age $= x^{2} . y e a r s$
$\Rightarrow$ Ashu's age after $5$ year $= (x + 5) y e a r s$
$\Rightarrow$ Ashu's mother age after $5$ year $= (x^{2} + 5) y e a r s$
According to the given condition,
$\Rightarrow$ $(x^{2} + 5) = 3 (x + 5)$
$\Rightarrow$ $x^{2} + 5 = 3 x + 15$
$\Rightarrow$ $x^{2} - 3 x - 10 = 0$
$\Rightarrow$ $x^{2} - 5 x + 2 x - 10 = 0$
$\Rightarrow$ $x (x - 5) + 2 (x - 5) = 0$
$\Rightarrow$ $(x - 5) (x + 2) = 0$
$\Rightarrow$ $x - 5 = 0$ and $x + 2 = 0$
$∴$ $x = 5$ and $x = - 2$
Age can not be negative.
$∴$ Ashu's age $= 5 y e a r s$
$\Rightarrow$ Ashu's mother age $= x^{2} = (5)^{2} = 25 y e a r s$
$\Rightarrow$ Required product $= 5 \times 25 = 125 y e a r s$

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Ashu is x years old while his mother Mrs Veena is x2 years old. Five years hence Mrs Veena will be three times old as Ashu. The product of their present ages is:

Ashu is x years old while his mother Mrs Veena is $x^{2}$ years old. Five years hence Mrs Veena will be three times old as Ashu. The product of their present ages is: