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. Find their present ages.

Given:

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.

To do:

We have to find their present ages.

Solution:

Age of Ashu after 5 years$=x+5$ years

Age of Mrs Veena after 5 years$=x^2+5$ years

According to the question,

$x^2+5=3(x+5)$

$x^2+5=3x+15$

$x^2-3x+5-15=0$

$x^2-3x-10=0$

Solving for $x$ by factorization method, we get,

$x^2-5x+2x-10=0$

$x(x-5)+2(x-5)=0$

$(x-5)(x+2)=0$

$x-5=0$ or $x+2=0$

$x=5$ or $x=-2$

Age cannot be negative. Therefore, the value of $x$ is $5$.

$x^2=(5)^2=25$

The present age of Ashu is $5$ years and the present age of Mrs Veena is $25$ years.

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Updated on: 10-Oct-2022

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