A and B invest ₹ 20,000 and ₹ 25,000, respectively. After 4 months, B leaves and C joins with ₹ 15,000 for the remaining 8 months. If the annual profit is ₹ 23,000, what is C's share?

Introduction / Context:
Partners coming and going change time weights. Profit must be shared by capital-time products across the year.

Given Data / Assumptions:

• A: 20,000 for 12 months.
• B: 25,000 for 4 months.
• C: 15,000 for 8 months.
• Total profit = ₹ 23,000.

Concept / Approach:
Compute weights for A, B, and C, convert to a simple ratio, then allocate profit accordingly.

Step-by-Step Solution:
A's weight = 20,000*12 = 2,40,000. B's weight = 25,000*4 = 1,00,000. C's weight = 15,000*8 = 1,20,000. Ratio = 12 : 5 : 6 (dividing by 20,000). Total parts = 23; each part = 23,000 / 23 = ₹ 1,000. C's share = 6 * 1,000 = ₹ 6,000.

Verification / Alternative check:
Shares: A = ₹ 12,000; B = ₹ 5,000; C = ₹ 6,000. Sum = ₹ 23,000, consistent.

Why Other Options Are Wrong:
They do not match the 12:5:6 weight split based on given durations.

Common Pitfalls:
Assuming all are invested for 12 months or forgetting that B leaves and C joins at specific times.

Final Answer:
₹ 6,000