Two partners invested ₹ 125000 and ₹ 85000 respectively in a business. They distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received ₹ 3000 more than the other, the total profit is

### Concept & Partial Profit Distribution When a portion of the profit is divided equally, it creates no difference in the final amounts received by the partners. Any difference in their final payouts stems entirely from the portion of the profit that is divided according to their investment ratio. ### Step-by-Step Solution * **Capital Ratio:** * $125000 : 85000$ * Divide by 5000: $25 : 17$ * **Analyzing Profit Distribution:** * Let the total profit be $P$. * 60% of $P$ is divided equally. This generates a difference of ₹ 0 between the partners. * 40% of $P$ is divided in the ratio $25 : 17$. This entirely accounts for the ₹ 3000 difference. * **Setting up the Equation:** * Let the 40% portion of the profit be distributed as $25x$ and $17x$. * The difference is $25x - 17x = 8x$. * We are given that the difference is ₹ 3000, so $8x = 3000$. * $x = \frac{3000}{8} = 375$. * **Finding Total Profit:** * The total amount for this 40% portion is $25x + 17x = 42x$. * $42x = 42 \times 375 = 15750$. * This means 40% of the total profit $P$ is ₹ 15750. * $0.40 \times P = 15750$ * $P = \frac{15750}{0.4} = 15750 \times 2.5 = 39375$. ### Exam Strategy & Shortcut Ignore the 60% immediately. The difference (8 ratio parts) equals 3000. Total ratio parts for the proportional split (42 parts) must be $42 \times \frac{3000}{8} = 15750$. Since 15750 is only 40% ($\frac{2}{5}$) of the total, multiply by $\frac{5}{2}$ to get 39375. ### Common Pitfall Trying to calculate 60% and 40% of an unknown variable $P$ simultaneously, creating a complex equation. Isolating the 40% component that causes the difference is much cleaner. ### Final Answer Therefore, the correct answer is **₹ 39375**.