A, B and C invest in a business in the ratio 3 : 6 : 5. A and C are working partners, while B is a sleeping partner whose share of profit is only three-fourths of what it would have been if he were a working partner. The firm earns a profit of Rs. 50,000, half of which is reinvested in the business and the remaining half is distributed among the partners. How much profit, in rupees, does C receive from this distributed amount?

Introduction / Context:
This partnership question tests understanding of how profit is shared when one partner is a sleeping partner whose share is reduced relative to working partners. The capital contribution ratio among A, B and C is given, and B does not work in the business. Only a part of the total profit is actually distributed, and we are asked to find C's share of this distributed profit. Such questions are important for exams on business mathematics and quantitative aptitude because they combine ratios, proportional reasoning and interpretation of conditions about working and sleeping partners.

Given Data / Assumptions:
- Capital ratio of A : B : C is 3 : 6 : 5.- A and C are working partners.- B is a sleeping partner and will receive only three-fourths of his normal profit share.- Total profit earned by the firm is Rs. 50,000.- Half of the profit is reinvested and half, that is Rs. 25,000, is distributed among the partners.- We need to find C's share in the distributed profit.

Concept / Approach:
The basic idea is that profit sharing is proportional to the product of capital and any adjustment factors, such as working or sleeping partner status. First, we interpret the ratio 3 : 6 : 5 as the base ratio of profits if all three were active working partners. Since B is a sleeping partner and receives only three-fourths of his normal share, we reduce B's share by multiplying his part of the ratio by 3/4. This produces an effective profit-sharing ratio. Finally, we apply this adjusted ratio to the portion of profit that is actually distributed, which is Rs. 25,000, and compute C's share.

Step-by-Step Solution:
Step 1: Base capital ratio is A : B : C = 3 : 6 : 5.Step 2: If B were a working partner, his profit share would be proportional to 6 parts. As a sleeping partner, he receives only three-fourths of that share.Step 3: Adjust B's ratio part: effective B part = 6 * (3/4) = 4.5.Step 4: The effective profit-sharing ratio becomes A : B : C = 3 : 4.5 : 5.Step 5: Sum of ratio parts = 3 + 4.5 + 5 = 12.5.Step 6: Out of Rs. 50,000 total profit, only half is distributed: distributed profit = 50,000 / 2 = Rs. 25,000.Step 7: C's share = (C's ratio part / total parts) * distributed profit.Step 8: C's share = (5 / 12.5) * 25,000.Step 9: 5 / 12.5 = 0.4, so C's share = 0.4 * 25,000 = Rs. 10,000.

Verification / Alternative check:
Check each partner's share using the effective ratio.Total units = 12.5; each unit = 25,000 / 12.5 = Rs. 2,000.A's share = 3 * 2,000 = Rs. 6,000.B's share = 4.5 * 2,000 = Rs. 9,000 (already reduced for sleeping status).C's share = 5 * 2,000 = Rs. 10,000.Sum = 6,000 + 9,000 + 10,000 = Rs. 25,000, which matches the distributed amount, so the calculation is consistent.

Why Other Options Are Wrong:
- 20000: This would imply C receives almost the entire distributed profit, which contradicts the given ratios and reduction for B.- 6000: This equals A's share, not C's, and comes from using 3 ratio parts instead of 5.- 9000: This is B's reduced sleeping-partner share, not C's share.

Common Pitfalls:
- Forgetting that only half of the total profit is distributed and not applying the ratio directly to Rs. 50,000.- Reducing B's ratio incorrectly by subtracting one-fourth instead of multiplying his share by three-fourths.- Adjusting the total profit instead of adjusting B's ratio part, which can make the ratio inconsistent.- Ignoring that A and C remain working partners whose shares are not reduced.

Final Answer:
The amount of profit that C receives from the distributed portion of Rs. 25,000 is Rs. 10,000.