Sharing profit when one partner gets a fixed fraction: A, B, and C share profit such that A receives 3/5 of the total, while B and C split the remaining equally. If C receives ₹ 400 less than A, find the total profit.

Introduction / Context: Here, the shares are specified in fractions of the whole: A has 3/5, and the remaining 2/5 is divided equally between B and C. A linear relation between A’s and C’s amounts is given (C is ₹ 400 less than A). Translate these to equations in the total profit T and solve for T directly.

Given Data / Assumptions:

• A = (3/5)T.
• B = C = (1/5)T.
• A − C = ₹ 400.

Concept / Approach: Substitute A and C in terms of T into the difference equation A − C = 400. This yields a simple equation in T; once T is known, all individual shares follow automatically.

Step-by-Step Solution:

Verification / Alternative check: Fractions sum: (3/5) + (1/5) + (1/5) = 1. Their values at T = 1,000 are ₹ 600, ₹ 200, ₹ 200, totaling ₹ 1,000.

Why Other Options Are Wrong: ₹ 1,200, ₹ 1,600, and ₹ 800 would yield A − C values other than ₹ 400; ₹ 2,000 doubles all shares and breaks the given difference condition.

Common Pitfalls: Assuming equal shares among all three or misreading “remaining profit equally” as “A, B, C equally.”

Final Answer: ₹ 1000