Question: User: 9.\tA and B formed a partnership and began operations on March 1, 20x1. A invested \u20a6400,000 cash, while B invested equipment with a book value of \u20a61,200,000 and a fair value of \u20a6720,000. On August 31, 20x1, A invested additional cash of \u20a680,000. The partnership agreement stipulates the following:\n\u2022\tMonthly salary allowances of \u20a68,000 and \u20a640,000 to A and B, respectively, recognized as expenses.\n\u2022\t20% bonus on profit before salaries and interest but after bonus to B. \n\u2022\t12% annual interest on the beginning capital of A.\n\u2022\tBalance equally.\n\nThe monthly salaries are withdrawn by the partners at each month-end. The partnership earned profit of \u20a6840,000 during the period before deductions for bonus and interest.\n\nHow much is the total share of B including salary allowances?
1. **State the problem:** Calculate the total share of B including salary allowances given the partnership details and profit.\n\n2. **Identify given data:**\n- A's initial cash investment = $400,000$\n- B's equipment fair value investment = $720,000$ (use fair value for capital)\n- A's additional cash on Aug 31 = $80,000$\n- Monthly salary allowances: A = $8,000$, B = $40,000$\n- Bonus to B = 20% on profit before salaries and interest but after bonus\n- Interest on A's beginning capital = 12% annual\n- Profit before deductions = $840,000$\n- Partnership period: March 1 to August 31 (6 months)\n\n3. **Calculate total salary allowances for B:**\n$$\text{B's salary} = 40,000 \times 6 = 240,000$$\n\n4. **Calculate interest on A's beginning capital:**\n- A's beginning capital = $400,000$\n- Interest rate = 12% annual\n- Time = 6 months = $\frac{6}{12} = 0.5$ year\n$$\text{Interest} = 400,000 \times 0.12 \times 0.5 = 24,000$$\n\n5. **Calculate bonus to B:**\nLet $x$ = bonus to B.\nProfit before salaries and interest but after bonus = $840,000 - x$\nBonus is 20% of this amount, so:\n$$x = 0.20 \times (840,000 - x)$$\n$$x = 168,000 - 0.20x$$\n$$x + 0.20x = 168,000$$\n$$1.20x = 168,000$$\n$$x = \frac{168,000}{1.20} = 140,000$$\n\n6. **Calculate profit after salaries, interest, and bonus:**\n- Total salaries = A's salary + B's salary = $8,000 \times 6 + 40,000 \times 6 = 48,000 + 240,000 = 288,000$\n- Interest on A's capital = $24,000$\n- Bonus to B = $140,000$\n\nProfit after these deductions:\n$$840,000 - 288,000 - 24,000 - 140,000 = 388,000$$\n\n7. **Calculate capital balances for sharing remaining profit:**\n- A's capital: initial $400,000 + 80,000$ additional = $480,000$\n- B's capital: $720,000$ (equipment fair value)\n\n8. **Calculate share of remaining profit:**\nBalance is shared equally, so each gets half:\n$$\frac{388,000}{2} = 194,000$$\n\n9. **Calculate total share of B:**\n- Salary allowance = $240,000$\n- Bonus = $140,000$\n- Share of remaining profit = $194,000$\n\nTotal share of B including salary allowances:\n$$240,000 + 140,000 + 194,000 = 574,000$$\n\n**Final answer:** B's total share including salary allowances is $\boxed{574,000}$.