A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profit will be only half of what it would have been if he were a working partner. The firm earns a total profit of Rs. 36,000, out of which 25% is reinvested in the business and the remaining 75% is distributed among the partners. How much does B receive, in rupees, from this distributed profit?

Introduction / Context:
This partnership problem involves three partners where one partner, C, is a sleeping partner and therefore receives a reduced share of the profit compared to what his capital ratio alone would entitle him to. The business also reinvests a portion of the profit, meaning that only the remaining part is actually distributed. The task is to calculate B's share of the distributed profit. This type of question strengthens understanding of effective profit-sharing ratios when modifications like sleeping partners and reinvestment occur.

Given Data / Assumptions:
- Capital investment ratio of A : B : C is 4 : 5 : 7.- C is a sleeping partner.- C's profit share is half of what it would have been if he were a working partner.- Total profit = Rs. 36,000.- 25% of the profit is reinvested in the business.- Thus, 75% of the total profit is distributed among the partners.- We must find B's share in the distributed profit.

Concept / Approach:
The solution requires adjusting the profit-sharing ratio to account for the reduced share of the sleeping partner. Initially, the ratio 4 : 5 : 7 represents the capital-based shares if everyone were working. For C, we cut his share to half by multiplying his ratio part by 1/2. This yields an effective profit-sharing ratio. We then apply this adjusted ratio to the amount actually distributed (75% of Rs. 36,000) to obtain each partner's share, and particularly B's share.

Step-by-Step Solution:
Step 1: Base profit-sharing ratio from capital is A : B : C = 4 : 5 : 7.Step 2: Since C is a sleeping partner, his share is half of his normal share.Step 3: C's effective part = 7 * (1/2) = 3.5.Step 4: Effective profit-sharing ratio becomes A : B : C = 4 : 5 : 3.5.Step 5: Sum of these effective parts = 4 + 5 + 3.5 = 12.5.Step 6: Total profit is Rs. 36,000. Only 75% is distributed because 25% is reinvested.Step 7: Distributed profit = 0.75 * 36,000 = Rs. 27,000.Step 8: B's share = (B's effective part / total effective parts) * distributed profit.Step 9: B's share = (5 / 12.5) * 27,000.Step 10: 5 / 12.5 = 0.4, so B's share = 0.4 * 27,000 = Rs. 10,800.

Verification / Alternative check:
Consider each unit of the effective ratio as representing an equal amount of profit.Total effective parts = 12.5, distributed profit = 27,000.Value per part = 27,000 / 12.5 = 2,160.A's share = 4 * 2,160 = 8,640.B's share = 5 * 2,160 = 10,800.C's share = 3.5 * 2,160 = 7,560.Total = 8,640 + 10,800 + 7,560 = 27,000, which matches the distributed profit, confirming our calculation.

Why Other Options Are Wrong:
- 7560: This corresponds approximately to C's effective share, not B's share.- 8640: This matches A's share rather than B's share based on the effective ratio.- 9200: This value does not correspond to any correct part multiple from the effective ratio and arises from incorrect percentage or ratio manipulation.

Common Pitfalls:
- Forgetting to reduce C's share by half and incorrectly using the original ratio 4 : 5 : 7.- Applying the ratio directly to the total profit of Rs. 36,000 instead of to the distributed portion of Rs. 27,000.- Miscalculating 25% and 75%, or using 25% as the distributed amount instead of the reinvested amount.- Treating 3.5 as 3 or 4 when simplifying the ratio, which distorts the final shares.

Final Answer:
B receives a profit share of Rs. 10,800 from the distributed amount.