Anu is a working partner and Bimla is a sleeping partner in a business. Anu puts in ₹ 5000 and Bimla puts in ₹ 6000. Anu receives 12.5% of the profit for managing the business and the rest is divided in proportion to their capitals. What does each get out of a profit of ₹ 880? (M.A.T., 2010)

### Concept & Working Partner Commission When a partnership includes a working partner, their management fee or commission is deducted from the total profit first. The remaining profit is then distributed among all partners (including the working partner) based on their capital investment ratio. ### Step-by-Step Solution * **Capital Ratio:** * Anu : Bimla = $5000 : 6000 = 5 : 6$ * **Anu's Management Fee:** * Anu receives 12.5% of the total profit. * $12.5\% = \frac{1}{8}$ * Fee = $\frac{1}{8} \times 880 = \text{₹ } 110$ * **Remaining Profit:** * Total Profit - Management Fee = $880 - 110 = \text{₹ } 770$ * **Distributing the Remainder:** * The remaining ₹ 770 is split in the ratio $5 : 6$. * Total ratio parts = $5 + 6 = 11$ * Value of 1 part = $\frac{770}{11} = \text{₹ } 70$ * Anu's investment share = $5 \times 70 = \text{₹ } 350$ * Bimla's investment share = $6 \times 70 = \text{₹ } 420$ * **Total Individual Earnings:** * Anu's Total = Management Fee + Investment Share = $110 + 350 = \text{₹ } 460$ * Bimla's Total = Investment Share = $\text{₹ } 420$ ### Exam Strategy & Shortcut Memorize fraction equivalents for common percentages to speed up calculations. Knowing that $12.5\% = \frac{1}{8}$ allows you to instantly calculate Anu's fee as $\frac{880}{8} = 110$ mentally. ### Common Pitfall Forgetting to add the working partner's management fee back to their investment share at the end. Anu gets *both* the ₹ 110 and the ₹ 350. ### Final Answer Therefore, the correct answer is **₹ 460, ₹ 420**.