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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?

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Solution

The correct option is **A**

16 years

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⇒(x−2)2=8x+68⇒x2+4−4x=8x+68⇒x2−12x−64=0⇒x2−16x+4x−64=0 [by splitting the middle term]⇒x(x−16)+4(x−16)=0⇒(x+4)(x−16)=0⇒x=16

[here, x≠−4 because his age cannot be negative]

Hence, Abhilash's present age is 16 years.

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