If x/2 years ago Adam was 12, and x/2 years from now he will be 2x yea

Solution:

Let us assume the current age of Adam be \(n\)

Adam's age \(\frac{x}{2}\) years ago, \(\frac{x}{2}\) years from now and \(3x\) years from now will be as follows:



We are given that Adam's age \(\frac{x}{2}\) years from now is 2x. Thus, we can write \(n+\frac{x}{2}=2x\)
\(⇒ n=2x-\frac{x}{2}\)
\(⇒ n=\frac{(4x-x)}{2}\)
\(⇒ n=\frac{3x}{2}\).........(i)

Next, we are given that Adam's age \(\frac{x}{2}\) years ago was 12. Thus, we can write \(n-\frac{x}{2}=12\)
\(⇒ \frac{3x}{2}-\frac{x}{2}=12\) (Plugging \(n=\frac{3x}{2}\))
\(⇒ \frac{2x}{2}=12\)
\(⇒ x=12\)

Plugging \(x=12\) in equation i we get:
\(n=\frac{3x}{2}\)
\(⇒n=\frac{(3\times 12)}{2}\)
\(⇒n=18\)

Finally, Adam's age \(3x\) years from now \(= n+3x\)
\(= 18+3\times 12\)
\(= 18+36 \)
\(= 54\)


Hence the right answer is Option A

Present age of Adam = 12 + x/2

Age of Adam after x/2 years = 12 + x

It is given that the age of Adam after x/2 years from now is 2x

Thus, 12 + x = 2x
x = 12.

Thus, present age of Adam = 12 + 12/2 = 18

After 3x years, i.e., after 36 years, age of Adam = 18+36 = 54.

Thus, the correct option is A.

assume Adam's present age = y
form two equation:
y- (x/2) = 12
y+(x/2) = 2x

after solving the equation:
x=12
y=18

ans= y+3x = 54

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