A, B, C subscribe ₹ 50000 for a business. A subscribes ₹ 4000 more than B and B ₹ 5000 more than C. Out of a total profit of ₹ 35000, A receives: (M.A.T., 2005)

### Concept & Investment Equations When total investment is given along with relative investments of partners, establish a single variable equation to find individual investments before calculating the profit ratio. ### Step-by-Step Solution * Let C's investment be $x$. * B subscribes ₹ 5000 more than C, so B's investment = $x + 5000$. * A subscribes ₹ 4000 more than B, so A's investment = $(x + 5000) + 4000 = x + 9000$. * Total investment = ₹ 50000 * $x + (x + 5000) + (x + 9000) = 50000$ * $3x + 14000 = 50000$ * $3x = 36000 \implies x = 12000$ * **Individual Investments:** * C = ₹ 12000 * B = $12000 + 5000 = \text{₹ } 17000$ * A = $12000 + 9000 = \text{₹ } 21000$ * **Profit Ratio:** * $A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12$ * **A's Share:** * Total ratio parts = $21 + 17 + 12 = 50$ * Total profit = ₹ 35000 * A's Share = $\frac{21}{50} \times 35000 = 21 \times 700 = 14700$ ### Exam Strategy & Shortcut To quickly solve the equation $3x + 14000 = 50000$, just subtract the extra amounts ($5000 + 9000 = 14000$) from the total ($50000$) to get $36000$, then divide by 3 to find the base amount $x = 12000$. ### Common Pitfall Setting up the relative equations backwards (e.g., making A = $x$ and subtracting). It is usually easiest to set the smallest investment (C in this case) as the variable $x$. ### Final Answer Therefore, the correct answer is **₹ 14700**.