Two partners invest Rs 12500 and Rs 8500 respectively in a business. They agree that 60% of the profit will be divided equally between them and the remaining 40% will be treated as interest on capital in proportion to their investments. If one partner receives Rs 240 more than the other, what is the total profit made in the business?

Introduction / Context:
This is a partnership profit sharing question that mixes two methods of distribution. A fixed percentage of profit is divided equally between partners, while the remaining percentage is distributed in the ratio of capital as a form of interest on capital. We are told the difference between final amounts received by the partners and must work backwards to determine the total profit for the business.

Given Data / Assumptions:
Two partners invest capitals Rs 12500 and Rs 8500. 60% of the profit is divided equally between them. 40% of the profit is shared in proportion to their capitals. One partner receives Rs 240 more than the other. We need to find the total profit.

Concept / Approach:
Let the total profit be P. Then 60% of P, or 0.6P, is shared equally, so each partner gets 0.3P from this part. The remaining 40% of P, or 0.4P, is shared in the ratio of capitals 12500 : 8500. Once we compute each partner share from this second part, we can express their total individual amounts and calculate the difference between them. Setting this difference equal to Rs 240 gives a simple equation that allows us to solve for P.

Step-by-Step Solution:
Step 1: Let total profit be P rupees. Step 2: 60% of P is shared equally, so each partner receives 0.3P from this part. Step 3: Remaining profit = 40% of P = 0.4P. Step 4: Capital ratio = 12500 : 8500. Divide both by 500 to simplify to 25 : 17. Step 5: From the 0.4P portion, partner 1 gets (25 / (25 + 17)) * 0.4P = (25 / 42) * 0.4P. Step 6: Partner 2 gets (17 / 42) * 0.4P. Step 7: Total share of partner 1 = 0.3P + (25 / 42) * 0.4P. Step 8: Total share of partner 2 = 0.3P + (17 / 42) * 0.4P. Step 9: Difference between their shares comes only from the second part and equals 0.4P * (25 / 42 - 17 / 42) = 0.4P * (8 / 42). Step 10: Simplify (8 / 42) to 4 / 21, so difference = 0.4P * 4 / 21 = 1.6P / 21. Step 11: Given the difference is Rs 240, so 1.6P / 21 = 240. Step 12: Multiply both sides by 21 to get 1.6P = 240 * 21 = 5040. Step 13: So P = 5040 / 1.6 = 3150.

Verification / Alternative check:
With total profit P = 3150, 60% part is 0.6 * 3150 = 1890, so each partner gets 945 from this part. The remaining 40% is 0.4 * 3150 = 1260. Dividing 1260 in the ratio 25 : 17 gives partner 1 share 1260 * 25 / 42 = 750 and partner 2 share 1260 * 17 / 42 = 510. Total for partner 1 = 945 + 750 = 1695, total for partner 2 = 945 + 510 = 1455. The difference is 1695 - 1455 = Rs 240, which matches the given difference, confirming that the total profit is Rs 3150.

Why Other Options Are Wrong:
If total profit were Rs 3250, Rs 4050 or Rs 3550, the difference computed using the same method would not equal 240. Each alternative total profit value produces a different difference between partner shares. Only P = Rs 3150 yields exactly Rs 240 difference, so the other options do not satisfy the conditions of the problem.

Common Pitfalls:
A common mistake is to distribute the entire profit only in proportion to capitals or only equally, ignoring the mixed rule. Another error is miscalculating the ratio part 25 : 17 or forgetting to divide the 0.4P portion correctly. Some learners also treat 60% and 40% as amounts rather than fractions of P. Keeping the two parts separate and carefully following the ratio calculations helps to avoid these errors.

Final Answer:
The total profit made in the business is Rs 3150.