A and B start an enterprise together, with A as the active partner. A invests Rs 4000 and invests an additional Rs 2000 after 8 months. B invests Rs 5000 and withdraws Rs 2000 after 9 months. Being the active partner, A also takes an allowance of Rs 100 per month from the profit. If the total profit for the year is Rs 6700, what is the share of B in the profit?

Introduction / Context:
This partnership question involves changing capitals over time and an active partner allowance taken from the profit. A invests more capital partway through the year, while B withdraws some capital after nine months. Additionally, A receives a fixed monthly allowance from the profit for managing the business. We need to find B final share of the profit after accounting for A allowance and capital time effect for both partners.

Given Data / Assumptions:
Total duration of the business is 12 months. A initially invests Rs 4000. A invests an additional Rs 2000 after 8 months, so his capital becomes Rs 6000 for the last 4 months. B invests Rs 5000 from the start and withdraws Rs 2000 after 9 months, so his capital becomes Rs 3000 for the last 3 months. A, being active partner, takes allowance of Rs 100 per month, that is 100 * 12 = Rs 1200 from the profit. Total profit before distribution is Rs 6700.

Concept / Approach:
We first deduct A allowance of Rs 1200 from the total profit to get the remaining profit to be shared in proportion to effective capital time contributions, or money months, of A and B. We compute money months separately for each phase where capitals remain constant. These values give us the ratio of A and B for profit sharing. Applying this ratio to the remaining profit yields the individual shares, from which we identify B part.

Step-by-Step Solution:
Step 1: Total profit is Rs 6700. A takes allowance of Rs 100 per month for 12 months, that is 100 * 12 = Rs 1200. Step 2: Remaining profit to be shared according to capital is 6700 - 1200 = Rs 5500. Step 3: For A, first 8 months capital is 4000, so money months = 4000 * 8 = 32000. Step 4: For last 4 months, A capital is 4000 + 2000 = 6000, so money months = 6000 * 4 = 24000. Step 5: Total money months of A = 32000 + 24000 = 56000. Step 6: For B, first 9 months capital is 5000, so money months = 5000 * 9 = 45000. Step 7: For last 3 months, B capital is 5000 - 2000 = 3000, so money months = 3000 * 3 = 9000. Step 8: Total money months of B = 45000 + 9000 = 54000. Step 9: Ratio of contributions A : B = 56000 : 54000. Step 10: Divide both terms by 2000, giving 28 : 27 as the simplified ratio. Step 11: Total ratio parts = 28 + 27 = 55 parts. Step 12: Share per part of the remaining profit = 5500 / 55 = Rs 100. Step 13: A share from remaining profit = 28 * 100 = Rs 2800, while B share = 27 * 100 = Rs 2700.

Verification / Alternative check:
We can confirm that the total distribution is consistent. A receives allowance Rs 1200 plus profit share Rs 2800, totalling Rs 4000. B receives Rs 2700. Combined, these sums are 4000 + 2700 = Rs 6700, which matches the original total profit. The ratio of 56000 : 54000 simplifies correctly to 28 : 27, verifying the basis for the profit split. This confirms B share is correctly calculated as Rs 2700.

Why Other Options Are Wrong:
If B share were Rs 3350, Rs 3250 or Rs 2800, the total distribution would no longer match Rs 6700 after also accounting for A allowance and capital contribution. These values would break the 28 : 27 ratio of money months or lead to an incorrect residual profit share for A. Only Rs 2700 fits both the ratio and the total profit condition.

Common Pitfalls:
One common error is to ignore A allowance and share the entire Rs 6700 by the 28 : 27 ratio. Another is to mistakenly treat capital changes as happening at the start of the year rather than after 8 or 9 months. Learners may also forget to break the year into segments with different capitals. Carefully separating allowance, subtracting it, and then computing money months for each phase prevents these mistakes.

Final Answer:
The share of B in the profit is Rs 2700.