1. **State the problem:** A can complete a work in 12 days, B can complete the same work in 18 days. They work together and get paid 6000 for the work. We need to find how much A should get. 2. **Formula and rules:** When two people work together, their combined work rate is the sum of their individual work rates. Work rate of A = $\frac{1}{12}$ work/day Work rate of B = $\frac{1}{18}$ work/day Combined work rate = $\frac{1}{12} + \frac{1}{18}$ 3. **Calculate combined work rate:** $$\frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}$$ 4. **Find the fraction of work done by A when working together:** Fraction of work done by A = $\frac{\text{A's rate}}{\text{combined rate}} = \frac{\frac{1}{12}}{\frac{5}{36}}$ Simplify: $$\frac{\frac{1}{12}}{\frac{5}{36}} = \frac{1}{12} \times \frac{36}{5} = \frac{36}{60} = \frac{3}{5}$$ 5. **Calculate A's share of the payment:** A's share = $\frac{3}{5} \times 6000 = 3600$ **Final answer:** A should get 3600.