smc

The item is bought for $24$ minus $12\frac{1}{2}\%$ of $24$. Since $12\frac{1}{2}\%=\frac{1}{8}$, the item was purchased for $24-24\cdot \frac{1}{8}$, or $21$. He wants to make $33\frac{1}{3}\%$ of the purchase price, or $21\cdot \frac{1}{3}=7$. This means the price must actually sell for $21+7=28$. If the article were marked for $x$ dollars, then after the $20\%$ discount, it would sell for $\frac{4}{5}x$. Thus, we have $\frac{4}{5}x=28$, which leads to $x=28\cdot \frac{5}{4}$, or $35$ dollars. The correct answer is $\boxed{\text{none of these}}$