Two businessmen A and B invest in a business in the ratio 5 : 8. They decide that 30% of the total profit will be reinvested into the business and only the remaining 70% will be distributed between them in the same ratio. If A's share of the distributed profit is Rs. 87,500, what was the total profit earned by the business, in rupees?

Introduction / Context:
This problem is based on a simple partnership scenario where two partners share profit in a fixed ratio but also choose to reinvest a part of the profit back into the business. The key idea is distinguishing between total profit and the portion that is actually distributed to the partners. Understanding this distinction and handling percentage and ratio calculations correctly is essential for solving such questions commonly asked in quantitative aptitude exams.

Given Data / Assumptions:
- Two partners A and B invest in the ratio 5 : 8.- Let total profit be P rupees.- 30% of the total profit is reinvested in the business.- Therefore, 70% of the total profit is distributed among A and B.- The distributed portion is shared in the ratio 5 : 8.- A's share from the distributed profit is Rs. 87,500.- We are required to find the total profit P.

Concept / Approach:
The approach involves two layers of proportional reasoning. First, only 70% of the profit is available for distribution. Second, that 70% is divided between A and B according to their capital ratio of 5 : 8. The share received by A is therefore a fixed fraction of the total profit. By expressing A's share in terms of P and equating it to Rs. 87,500, we can solve a simple linear equation to obtain the value of P.

Step-by-Step Solution:
Step 1: Let total profit be P.Step 2: Reinvestment is 30% of P, so distributed profit = 70% of P.Step 3: Therefore, distributed profit = 0.70 * P.Step 4: This distributed amount is shared in the ratio 5 : 8, so total ratio parts = 5 + 8 = 13.Step 5: A's share = (5 / 13) of the distributed profit.Step 6: Hence, A's share = (5 / 13) * 0.70 * P.Step 7: Note that 0.70 = 7 / 10, so A's share = (5 / 13) * (7 / 10) * P = (35 / 130) * P = (7 / 26) * P.Step 8: We are given A's share = Rs. 87,500, so (7 / 26) * P = 87,500.Step 9: Solve for P: P = 87,500 * (26 / 7).Step 10: 87,500 * 26 = 2,275,000 and dividing by 7 gives P = 325,000.Therefore, the total profit is Rs. 3,25,000.

Verification / Alternative check:
Take P = 325,000.Distributed profit = 70% of 325,000 = 0.70 * 325,000 = 227,500.A's share = (5 / 13) * 227,500.Compute: 227,500 / 13 = 17,500 and 17,500 * 5 = 87,500.This matches the given information, so the result is consistent.

Why Other Options Are Wrong:
- 227000: This is close to the distributed profit, not the total profit, and ignores the reinvested portion.- 250000: This would give a smaller distributed amount and therefore a smaller share for A than 87,500.- 375000: This would produce an A share larger than 87,500 if calculated correctly, so it does not fit the data.

Common Pitfalls:
- Treating Rs. 87,500 as A's share out of the entire profit rather than from the 70% portion.- Using the ratio 5 : 8 directly on the total profit P instead of on the distributed profit only.- Mistakes in handling percentages, especially not converting 30% reinvestment into 70% distribution correctly.- Arithmetic errors when solving (7 / 26) * P = 87,500.

Final Answer:
The total profit earned by the business was Rs. 3,25,000.