1. **State the problem:** X, Y, and Z invested 12000, 8000, and 10000 respectively in a business. Z received 2500 as his share of the profit. We need to find X's and Y's shares of the profit. 2. **Understand the concept:** Profit is divided in the ratio of their investments. So, the ratio of X:Y:Z = 12000:8000:10000. 3. **Simplify the ratio:** Divide each by 4000: $$\frac{12000}{4000} : \frac{8000}{4000} : \frac{10000}{4000} = 3 : 2 : 2.5$$ 4. **Express Z's share in terms of the ratio:** Let the common ratio factor be $k$. Then Z's share = $2.5k$. Given Z's share = 2500, so: $$2.5k = 2500$$ 5. **Solve for $k$:** $$k = \frac{2500}{2.5} = 1000$$ 6. **Find X's share:** $$X = 3k = 3 \times 1000 = 3000$$ 7. **Find Y's share:** $$Y = 2k = 2 \times 1000 = 2000$$ **Final answer:** X's share of the profit is 3000. Y's share of the profit is 2000.