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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?


A

16 years

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B

50 years

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C

20 years

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D

29 years

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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.
(x2)2=8x+68(x2)2=8x+68x2+44x=8x+68x212x64=0x216x+4x64=0 [by splitting the middle term]x(x16)+4(x16)=0(x+4)(x16)=0x=16
[here, x4 because his age cannot be negative]
Hence, Abhilash's present age is 16 years.


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