Question

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.

Answer 1

Given that Ashu’s present age is x years and his mother Mrs. Veena is x² years

Then according to question,

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

And his mother Mrs. Veena is  = (x² + 5) years

Thus

x² + 5 = 3(x + 5)

x² + 5 = 3x + 15

x² + 5 - 3x - 15 = 0

x² - 3x - 10 = 0

x² - 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

x² = (5)² = 25

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