1. Let's start by defining the total profit as $12000$. 2. The businessman said he used $\frac{1}{3}$ of the profit. Calculate this part: $$\frac{1}{3} \times 12000 = 4000$$ 3. Subtract this used amount from the total profit to find the remainder: $$12000 - 4000 = 8000$$ 4. He said he used $\frac{1}{5}$ of the remainder for something else (possibly "history" which we interpret as another use). Calculate $\frac{1}{5}$ of $8000$: $$\frac{1}{5} \times 8000 = 1600$$ 5. Calculate what is left after using $1600$ from the remainder: $$8000 - 1600 = 6400$$ 6. According to the problem, he used the rest, amounting to $4800$, for food powder, but our calculation shows the rest as $6400$. Since the problem states the used amount for food powder as $4800$, let's clarify that $4800$ is the actual money used for food powder. 7. Therefore, the money used to improve the business would be the amount used on $\frac{1}{5}$ of the remainder, which is $1600$. **Final answer:** The businessman used $1600$ to improve his business.