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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.
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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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