Comparing profit shares after staggered changes and a late entrant: A invests ₹ 16,000; B invests ₹ 12,000. After 3 months, A withdraws ₹ 5,000 (so ₹ 11,000 thereafter), B adds ₹ 5,000 (so ₹ 17,000 thereafter). After another 3 months (at month 6), C joins with ₹ 21,000 for the last 6 months. If total profit after 12 months is ₹ 26,400, by how much does B’s share exceed C’s share?

Introduction / Context: This advanced partnership problem involves multiple changes in capitals over time and a new partner joining mid-year. The correct approach is to compute each partner’s money-months by segments and then apply proportional sharing of the total profit. Finally, compare B’s and C’s rupee shares.

Given Data / Assumptions:

• Months 0–3: A = ₹ 16,000; B = ₹ 12,000; C = ₹ 0.
• Months 3–6: A = ₹ 11,000; B = ₹ 17,000; C = ₹ 0.
• Months 6–12: A = ₹ 11,000; B = ₹ 17,000; C = ₹ 21,000.
• Total profit = ₹ 26,400.

Concept / Approach: Compute money-months for each partner by summing capital × months over segments, form total weights, and multiply the total profit by each partner’s weight fraction to obtain their shares. The required answer is B’s share minus C’s share.

Step-by-Step Solution:

Verification / Alternative check: A share = 26,400 − (10,800 + 7,200) = ₹ 8,400. The ratio 8,400 : 10,800 : 7,200 reduces to 7 : 9 : 6, which matches 1,47,000 : 1,89,000 : 1,26,000 after dividing by 21,000.

Why Other Options Are Wrong: ₹ 1,200, ₹ 2,400, ₹ 4,800, and ₹ 3,000 do not follow from the exact weight fractions and produce inconsistencies with the total profit.

Common Pitfalls: Forgetting to break the year into segments; misplacing when C joins; or using average capitals rather than exact segment sums.

Final Answer: Rs. 3600