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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.
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