Explanation:

- The problem states that when a number is increased by 32, it becomes 116% of itself.

- Let's denote the original number as $x$.

- The equation can be written as: $x+32=1.16x$.

- Rewriting, we get: $x+32=1.16x$ or $32=1.16x-x$.

- Simplifying, we find $32=0.16x$.

- Solving for $x$, we get $x=\frac{32}{0.16}$.

- This results in $x=200$.

- Option 1: 384 – Not correct, does not satisfy the equation.

- Option 2: 480 – Not correct, does not satisfy the equation.

- Option 3: 200 – Correct, solves the equation perfectly.

- Option 4: 288 – Not correct, does not satisfy the equation.