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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. Find Their Present Ages. - CBSE Class 10 - Mathematics

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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.

Solution

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.

  Is there an error in this question or solution?

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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.
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