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: Represent the ages algebraically.
Let Sonu's present age be \(x\) years.
His age 3 years ago was \(x-3\), so double that age is \(2(x-3)\).
His age 2 years hence (from now) is \(x+2\), so twice that age is \(2(x+2)\).

Step 2: Translate the sentence into an equation.
"Doubled and subtracted from twice his age 2 years hence" means we take twice the future age and subtract twice the past age from it:
\[ 2(x+2) - 2(x-3) = \text{resultant} \]
This resultant is said to be exactly half of his present age:
\[ 2(x+2) - 2(x-3) = \frac{x}{2} \]

Step 3: Simplify the left side.
\[ 2x+4 - (2x-6) = \frac{x}{2} \]
\[ 2x+4-2x+6 = \frac{x}{2} \]
\[ 10 = \frac{x}{2} \]
Notice the \(x\) terms cancel on the left, so the left side always comes out to a fixed number no matter what \(x\) is; this is what makes the equation solvable directly.

Step 4: Solve for \(x\).
\[ x = 10 \times 2 = 20 \]

Step 5: Verify and rule out the others.
At \(x=20\): age 3 years ago is 17, doubled is 34. Age 2 years hence is 22, twice is 44. \(44-34=10\), and half of 20 is also 10, so it checks out.
Option (a) 15 does not satisfy this since the left side is always 10 regardless of \(x\), while half of 15 is 7.5, not 10. Option (c) 24 gives half as 12, not 10. So only \(x=20\) works, and option (d) is not needed.

Final Answer:
Sonu's present age is 20 years.
\[ \boxed{20 \text{ years}} \]