Question

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?

Answer 1

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.
\((x - 2)^2 = 8x+68\\
\Rightarrow (x - 2)^2 = 8x + 68\\
\Rightarrow x^2 + 4 - 4x = 8x + 68\\
\Rightarrow x^2 - 12x - 64 =0\\
\Rightarrow x^2 - 16x + 4 x - 64 = 0~~~~[by~ splitting~ the~ middle ~term]\\
\Rightarrow x(x - 16) + 4(x - 16) =0\\
\Rightarrow (x + 4)(x - 16) = 0\\
\Rightarrow x = 16\)
[here, \(x \neq -4\) because his age cannot be negative]
Hence, Abhilash's present age is 16 years.