If two years ago the square of Animesh's age (in years) was 68 more than 8 times his actual age, then find his present age.

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Solution

Let the actual age of Animesh be $x$ years
His age when he was 2 years younger = (x - 2) years
Now, by given condition,
Square of his age = 68 more than 8 times her actual age.
i.e., $(x - 2)^{2} = 8 x + 68 \Rightarrow (x - 2)^{2} = 8 x + 68 \Rightarrow x^{2} + 4 - 4 x = 8 x + 68 \Rightarrow x^{2} - 12 x - 64 = 0 \Rightarrow x^{2} - 16 x + 4 x - 64 = 0 [by~ splitting~ the~ middle ~term] \Rightarrow x (x - 16) + 4 (x - 16) = 0 \Rightarrow (x + 4) (x - 16) = 0 \Rightarrow x = 16$

[here, $x \neq - 4$ because his age cannot be negative]

Hence, Animesh's present age is 16 years.

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