A is the working partner and B is the sleeping partner. A invests ₹ 12,000 and B invests ₹ 20,000. A receives 10% of the profit as a managing commission, and the remainder is divided in the ratio of their capitals. If the total profit is ₹ 9,600, how much does A receive in total?

Introduction / Context: Mixed distribution rules are common in partnership questions: a fixed percentage to the managing partner first, with the balance divided according to capital ratios. The order matters.

Given Data / Assumptions:

• Total profit = ₹ 9,600.
• Managing commission to A = 10% of total profit.
• Remaining profit split by capital ratio 12,000 : 20,000 = 3 : 5.

Concept / Approach: First take 10% of total for A. Then divide the remainder in 3 : 5, add A's two components to get the total received by A.

Step-by-Step Solution: Commission to A = 10% of 9,600 = ₹ 960. Remainder = 9,600 − 960 = ₹ 8,640. A's share of remainder = 3/8 of 8,640 = ₹ 3,240. Total to A = 960 + 3,240 = ₹ 4,200.

Verification / Alternative check: B's share of the remainder = 5/8 of 8,640 = ₹ 5,400; combined with A's 4,200 gives the full ₹ 9,600.

Why Other Options Are Wrong: ₹ 3,240 and ₹ 3,600 exclude the commission; ₹ 4,500 and ₹ 4,000 misuse the sequence or ratio.

Common Pitfalls: Splitting the entire profit by the ratio first, or applying the 10% on the remainder instead of the total profit.

Final Answer: ₹ 4,200