If Abhilash was younger by 2 years than what he really is, then the square of his age (in years) would have been 68 more than 8 times his actual age. What is his age now?

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Solution

Let the actual age of Abhilash = 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.
$(x - 2)^{2} = 8 x + 68 \Rightarrow (x - 2)^{2} = 8 x + 68 \Rightarrow x^{2} + 4 - 4 x = 8 x + 68 \Rightarrow x^{2} - 12 x - 64 = 0 \Rightarrow x^{2} - 16 x + 4 x - 64 = 0 [b y s p l i t t i n g t h e m i d d l e t e r m] \Rightarrow x (x - 16) + 4 (x - 16) = 0 \Rightarrow (x + 4) (x - 16) = 0 \Rightarrow x = 16$
[here, $x \neq - 4$ because his age cannot be negative]
Hence, Abhilash's present age is 16 years.

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