A, B and C entered into a partnership. A invested ₹ 2560 and B invested ₹ 2000. At the end of the year, they gained ₹ 1105, out of which A got ₹ 320. C's capital was (S.S.C., 2006)

### Concept & Total Capital Calculation When all investments are made for the same duration, the ratio of individual profit to total profit is identical to the ratio of individual capital to total capital. $$ \frac{\text{A's Capital}}{\text{Total Capital}} = \frac{\text{A's Profit}}{\text{Total Profit}} $$ ### Step-by-Step Solution * Since the time period is the same for all (1 year), the profit shares depend strictly on the initial capital amounts. * **Set up the Proportion:** * A's Capital = ₹ 2560 * A's Profit = ₹ 320 * Total Profit = ₹ 1105 * Let Total Capital be $T$. * $\frac{2560}{T} = \frac{320}{1105}$ * **Solve for Total Capital:** * $T = \frac{2560 \times 1105}{320}$ * $T = 8 \times 1105 = 8840$ * **Find C's Capital:** * Total Capital = A's Capital + B's Capital + C's Capital * $8840 = 2560 + 2000 + \text{C's Capital}$ * $8840 = 4560 + \text{C's Capital}$ * C's Capital = $8840 - 4560 = 4280$ ### Exam Strategy & Shortcut Find the multiplier linking A's profit to A's capital. $320 \times 8 = 2560$. This multiplier (8) applies to the entire business. So, Total Capital = $8 \times 1105 = 8840$. Subtract A and B's known capitals ($2560 + 2000 = 4560$) from 8840 to get C's capital (4280) immediately. ### Common Pitfall Trying to determine the profit shares of B and C individually first. It is an unnecessary middle step that wastes time when you only need total capital to find C's missing piece. ### Final Answer Therefore, the correct answer is **₹ 4280**.