Partners A, B, and C have invested Rs.5000, Rs.6000, and Rs.4000 respectively in a business. A receives 30% of the total profit as a management fee. The remaining profit is shared among all three partners in proportion to their investments. At the end of the year, A's profit exceeds the combined profits of B and C by Rs.200. What is the total profit earned?

Explanation

The capital ratio of A, B, and C is 5:6:4. A receives 30% of the total profit upfront. The remaining 70% is divided based on their capital ratio. Let the total profit be P. Then, A's share = 30% of P + (5/15) of 70% of P = 0.3P + (5/15)(0.7P) = 0.3P + 0.2333P = 0.5333P. The combined share of B and C = total profit - A's share = P - 0.5333P = 0.4667P. According to the problem, A's profit is Rs.200 more than B and C combined: 0.5333P - 0.4667P = 200, which simplifies to 0.0666P = 200. Solving for P gives P = Rs.3000.