What is $50\%$ of $200\%$ of $10$?
To solve this problem, I need to find out what $200\%$ of $10$ is first, and then take half of that. I know that $200\%$ of something means doubling it, so $200\%$ of $10$ is just $2 \times 10 = 20$. Now I need to find $50\%$ of $20$, which means halving it, so $50\%$ of $20$ is $0.5 \times 20 = 10$. Therefore, the final answer is $10$.

