Staggered investments and a new partner: A and B invest ₹ 16000 and ₹ 12000. After 3 months, A withdraws ₹ 5000 while B adds ₹ 5000. After 3 more months, C joins with ₹ 21000. At year-end, the profit is ₹ 13200. By how much does B’s share exceed C’s share?

Introduction / Context:
This partnership problem combines changing capitals over time and the entry of a new partner. The profit split must respect the money–time products across the distinct periods of the year.

Given Data / Assumptions:

• Months 1–3: A = 16000, B = 12000.
• Months 4–6: A = 11000, B = 17000.
• Months 7–12: A = 11000, B = 17000, C = 21000.
• Total profit = ₹ 13200.

Concept / Approach:
Compute each partner’s weight = sum of (capital * months) over relevant periods. Then divide the profit proportionally. Finally, compute the excess of B’s share over C’s share.

Step-by-Step Solution:
A's weight = 16000*3 + 11000*3 + 11000*6 = 48000 + 33000 + 66000 = 147000.B's weight = 12000*3 + 17000*3 + 17000*6 = 36000 + 51000 + 102000 = 189000.C's weight = 21000*6 = 126000.Total weight = 147000 + 189000 + 126000 = 462000.Per-weight profit = 13200 / 462000 = 1/35.B's share = 189000 / 35 = ₹ 5400; C's share = 126000 / 35 = ₹ 3600.Difference = ₹ 5400 − ₹ 3600 = ₹ 1800.

Verification / Alternative check:
The weights reduce in the ratio 147 : 189 : 126 = 7 : 9 : 6. Total parts 22; profit per part = 13200/22 = 600. Then A = 7*600 = 4200, B = 9*600 = 5400, C = 6*600 = 3600; difference 1800, consistent.

Why Other Options Are Wrong:

• ₹ 1600, ₹ 2100, and ₹ 2300 do not match the exact weight-based calculation.

Common Pitfalls:

• Not splitting the year into correct 3–3–6 month blocks.
• Forgetting A’s withdrawal and B’s addition when computing later-period weights.

Final Answer:
₹ 1800