A and B start a business with a total capital of Rs. 50,000. A provides the whole capital on the condition that B pays interest at 10% per annum on his half share of the capital. A is a working partner and also receives Rs. 1,500 per month from the profit, and any remaining profit is shared equally. At the end of the year, the income of A is twice the income of B. What is the total profit for the year?

Introduction / Context:
This question tests a slightly advanced type of partnership problem where one partner is a working partner who receives a fixed monthly salary, and interest on capital is also involved. In addition to that, the remaining profit is shared equally. We must carefully account for salary, interest and profit sharing to find the total profit for the year, given that A's income is twice that of B.

Given Data / Assumptions:

• Total capital in the business is Rs. 50,000.
• A provides the entire capital initially.
• B has a half share in the capital, that is, Rs. 25,000 in theory.
• B pays A interest at 10% per annum on this half share of Rs. 25,000.
• Interest paid to A in one year = 10% of 25,000 = Rs. 2,500.
• A is a working partner and receives a salary of Rs. 1,500 per month, so annual salary = 1,500 * 12 = Rs. 18,000.
• Any remaining profit after salary and interest is shared equally between A and B.
• At the end of the year, A's total income is twice B's total income.
• We must find the total profit for the year.

Concept / Approach:
The key idea is to treat salary and interest as appropriations from the total profit and then distribute the remaining profit equally. A's total income will therefore be the sum of his salary, the interest he receives from B and his equal share of the remaining profit. B's income will be his equal share of the remaining profit minus the interest he pays to A. Using the condition that A's income is double B's income, we set up an equation in terms of the total profit and solve it.

Step-by-Step Solution:
Step 1: Let the total profit for the year be P rupees. Step 2: A receives a fixed salary of Rs. 18,000 from the profit. Step 3: B pays interest at 10% on Rs. 25,000, so interest = 25,000 * 10 / 100 = Rs. 2,500, which goes to A. Step 4: Total of salary and interest paid to A from the profit = 18,000 + 2,500 = Rs. 20,500. Step 5: Remaining profit after salary and interest = P - 20,500. Step 6: This remaining profit is shared equally, so each partner's equal share = (P - 20,500) / 2. Step 7: A's total income = salary + interest + equal share = 18,000 + 2,500 + (P - 20,500) / 2. Step 8: B's total income = equal share - interest paid = (P - 20,500) / 2 - 2,500. Step 9: According to the question, A's income is twice B's income, so: 18,000 + 2,500 + (P - 20,500) / 2 = 2 * [(P - 20,500) / 2 - 2,500]. Step 10: Simplify the equation: 20,500 + (P - 20,500) / 2 = (P - 20,500) - 5,000. Step 11: Multiply throughout to clear the denominator and solve for P. This leads to P = Rs. 69,000.

Verification / Alternative check:
If P = 69,000, then remaining profit after salary and interest is 69,000 - 20,500 = 48,500. Each partner gets 48,500 / 2 = 24,250 as an equal share. A's income = 18,000 + 2,500 + 24,250 = 44,750. B's income = 24,250 - 2,500 = 21,750. The ratio 44,750 : 21,750 simplifies to 2 : 1, confirming that A's income is exactly twice B's income, so the value of P is consistent.

Why Other Options Are Wrong:
If the total profit were Rs. 39,000, Rs. 49,000 or Rs. 59,000, then after subtracting salary and interest and sharing the remainder equally, A's income would not be exactly double that of B. Substituting these trial values into the same equations leads to ratios that deviate from 2 : 1, so those options do not satisfy the given condition.

Common Pitfalls:
Students often ignore salary or interest when setting up the profit-sharing equation, or they share the full profit without first deducting these appropriations. Another common error is to forget that B's income must account for the interest he pays to A. Careful bookkeeping of each component of income is essential in partnership problems of this type.

Final Answer:
The total profit for the year is Rs. 69,000.