Partnership with time-weighted capitals and a mid-year change: Amitabh, Brijesh, and Kamlesh begin a partnership with initial capital shares in the ratio 7/2 : 4/3 : 6/5, respectively. After 4 months, Amitabh increases his capital by 50% for the remaining 8 months of the year. If the total profit at the end of 12 months is ₹ 21600, determine Brijesh’s share of the profit.

Introduction / Context:
This partnership question tests the time-weighted capital concept. Profits are divided in the ratio of (capital * time). Since Amitabh increases his capital after 4 months, we must split his contribution into two time blocks and then compare with Brijesh and Kamlesh who keep their capitals unchanged throughout the year.

Given Data / Assumptions:

• Initial capital ratio: Amitabh : Brijesh : Kamlesh = 7/2 : 4/3 : 6/5.
• Amitabh invests 7/2 units for the first 4 months, then increases by 50% to 21/4 units for the next 8 months.
• Brijesh invests 4/3 units for all 12 months.
• Kamlesh invests 6/5 units for all 12 months.
• Total profit = ₹ 21600.

Concept / Approach:
Compute each partner’s money–time product and use these as weights to split the profit. For Amitabh, compute two segments due to the 50% increase. For Brijesh and Kamlesh, multiply their capitals by 12 months directly.

Step-by-Step Solution:
Amitabh's weight = (7/2)*4 + (21/4)*8 = 14 + 42 = 56.Brijesh's weight = (4/3)*12 = 16.Kamlesh's weight = (6/5)*12 = 72/5 = 14.4.Total weight = 56 + 16 + 14.4 = 86.4.Brijesh's share = 21600 * (16 / 86.4) = 21600 * (1 / 5.4) ≈ 4000 (exactly 4000 since 86.4 * 250 = 21600).

Verification / Alternative check:
Since 86.4 × 250 = 21600, the per-weight share is 250. Brijesh has 16 weights, so 16 × 250 = ₹ 4000, which matches our computation precisely.

Why Other Options Are Wrong:

• ₹ 8000 and ₹ 12000 are too large relative to Brijesh’s smaller weight compared to Amitabh.
• ₹ 7000 does not match the exact weight-based split.

Common Pitfalls:

• Forgetting to split Amitabh’s capital into two time periods after his 50% increase.
• Dividing by simple capital ratios without multiplying by months.

Final Answer:
₹ 4000