A starts with ₹ 4,000 for 12 months; B joins after 3 months with ₹ 8,000 for 9 months; C invests ₹ 20,000 but only for the last 2 months. At year end, profit is ₹ 16,800. How should the profit be divided among A, B, and C?

Introduction / Context:
Different start times and durations require capital-time weights for each partner. Profit division then follows those weights.

Given Data / Assumptions:

• A: 4,000 for 12 months.
• B: 8,000 for 9 months.
• C: 20,000 for 2 months.
• Total profit = ₹ 16,800.

Concept / Approach:
Compute weights: A = 4,000*12, B = 8,000*9, C = 20,000*2. Reduce to a simple ratio and split the profit accordingly.

Step-by-Step Solution:
A's weight = 48,000; B's weight = 72,000; C's weight = 40,000. Ratio = 48,000 : 72,000 : 40,000 = 6 : 9 : 5. Total parts = 6 + 9 + 5 = 20; each part = 16,800 / 20 = ₹ 840. Shares: A = 6*840 = ₹ 5,040; B = 9*840 = ₹ 7,560; C = 5*840 = ₹ 4,200.

Verification / Alternative check:
Sum = 5,040 + 7,560 + 4,200 = ₹ 16,800, confirming the division.

Why Other Options Are Wrong:
Options that swap roles or change one figure break the 6 : 9 : 5 ratio implied by the investment schedule.

Common Pitfalls:
Forgetting C invests only for 2 months, or mistakenly assuming all invested for the full year.

Final Answer:
A = ₹ 5,040, B = ₹ 7,560, C = ₹ 4,200