Explanation:

- Start with an initial number, let's call it $x$.

- Increasing $x$ by 15% gives: $x\times 1.15$.

- Reducing the new amount by 15% gives: $x\times 1.15\times 0.85=782$.

- Solving $x\times 0.9775=782$, we find $x=800$.

Now with the same number, perform other operations:

- Reduce 800 by 25%: $800\times 0.75=600$.

- Increase 600 by 25%: $600\times 1.25=750$.

- Finally, reduce 750 by 20%: $750\times 0.8=600$.

- The resulting number is 600, corresponding to:

- Option 4: 600