Question

When Sonu's age 3 years ago is doubled and subtracted from twice his age 2 years hence, the resultant is exactly half of his present age. Find his present age (in years).

• A. 15
• B. 20
• C. 24
• D. None of these

Hint:

Write \(2(x+2)-2(x-3)\) and notice the \(x\) terms cancel, leaving a fixed number equal to \(\frac{x}{2}\).

Answer 1

The Correct Option is B

Step 1: Test the given options directly in the word statement.
Instead of building the equation first, we can check each candidate age against the sentence: "twice his age 2 years hence minus twice his age 3 years ago equals half his present age."

Step 2: Try option (a), $x = 15$.
Age 3 years ago $= 12$, doubled $= 24$. Age 2 years hence $= 17$, twice $= 34$.
$34 - 24 = 10$. Half of present age $= 7.5$. Since $10 \ne 7.5$, this option fails.

Step 3: Try option (b), $x = 20$.
Age 3 years ago $= 17$, doubled $= 34$. Age 2 years hence $= 22$, twice $= 44$.
$44 - 34 = 10$. Half of present age $= 10$. Since $10 = 10$, this option satisfies the condition exactly.

Step 4: Try option (c), $x = 24$, to confirm it fails.
Age 3 years ago $= 21$, doubled $= 42$. Age 2 years hence $= 26$, twice $= 52$.
$52 - 42 = 10$. Half of present age $= 12$. Since $10 \ne 12$, this option fails.

Step 5: Notice the pattern and conclude.
In every case, twice the future age minus twice the past age equals a constant value of 10, since the $x$ terms always cancel. So the only age that can work is the one where half the present age also equals 10, which is $x = 20$. Option (d) is therefore not required.
\[ \boxed{20 \text{ years}} \]