1. State the problem: A businessman made a profit of $12000$. He saved $\frac{1}{3}$ of this profit, used $\frac{3}{5}$ of the remainder for food, and used the rest to improve his business. We need to find how much money he used for food. 2. Calculate the amount saved: $$\text{Saved} = \frac{1}{3} \times 12000 = 4000$$ 3. Calculate the remainder after saving: $$\text{Remainder} = 12000 - 4000 = 8000$$ 4. Calculate the amount used for food: $$\text{Food} = \frac{3}{5} \times 8000 = 4800$$ 5. Final answer: The businessman used $4800$ for food.