#### Question

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.

#### Solution

Given that Ashu’s present age is x years and his mother Mrs. Veena is x^{2} years

Then according to question,

Five years later, Ashu’s is = (x + 5) years

And his mother Mrs. Veena is = (x^{2} + 5) years

Thus

x^{2} + 5 = 3(x + 5)

x^{2} + 5 = 3x + 15

x^{2} + 5 - 3x - 15 = 0

x^{2} - 3x - 10 = 0

x^{2} - 5x + 2x - 10 = 0

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

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

So, either

x - 5 = 0

x = 5

Or

x + 2 = 0

x = -2

But, the age can never be negative.

Therefore, when x = 5 then

x^{2} = (5)^{2} = 25

Hence, Ashu’s present age is 5years and his mother Mrs. Veena is 25 years.

Is there an error in this question or solution?

#### APPEARS IN

Solution 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. Find Their Present Ages. Concept: Solutions of Quadratic Equations by Factorization.