The answer is A: $20 \%$ is withheld for income taxes.
Explanation for each option:
A. $20 \%$ is withheld for income taxes - This is the correct answer. When an individual receives eligible rollover funds directly from a profit-sharing plan, the IRS requires that 20% of the distribution be withheld for federal income taxes if the funds are not directly rolled over to another qualified retirement plan or IRA.
B. $30 \%$ is withheld for income taxes - This is incorrect. The standard withholding rate for eligible rollover distributions not directly rolled over is 20%, not 30%.
C. $10 \%$ is withheld for income taxes - This is incorrect. The withholding rate for eligible rollover distributions is 20%, not 10%.
D. Nothing is withheld - This is incorrect. If the distribution is paid directly to the participant and not rolled over, 20% must be withheld for federal income taxes.
In summary, when an individual personally receives eligible rollover funds from a profit-sharing plan, 20% is withheld for income taxes unless the funds are directly rolled over to another qualified plan or IRA.