A and B started a business and distribute the profit at the end of the year. Both also receive individual salaries from the total profit before the remaining profit is distributed. A's salary is 16% of the remaining profit after paying B's salary. B's salary is 16.67% of the total profit. If A received a total of Rs. 11,000 and the profit-sharing ratio between A and B is 1:2, find the total profit for the year (in thousands of rupees).

Let's break down the problem step by step:

### 1. Defining Variables:
- Let the **total profit** be \( P \) (in thousands of rupees).
- B's salary is given as 16.67% of the total profit. Therefore, B's salary is:
  \[
  \text{B's Salary} = 0.1667P
  \]
- A's salary is 16% of the remaining profit after paying B's salary. The remaining profit after paying B's salary is:
  \[
  \text{Remaining Profit} = P - 0.1667P = 0.8333P
  \]
  So, A's salary is 16% of this remaining profit:
  \[
  \text{A's Salary} = 0.16 \times 0.8333P = 0.1333P
  \]

### 2. Total Amount A Received:
The total amount A received consists of two parts:
- A's salary of \( 0.1333P \), and
- A's share of the remaining profit.

After both salaries are deducted, the remaining profit is:
\[
\text{Remaining Profit After Salaries} = P - (0.1667P + 0.1333P) = 0.7P
\]
A and B share this remaining profit in the ratio of 1:2. Therefore, A's share of the remaining profit is:
\[
\text{A's Share} = \frac{1}{3} \times 0.7P = 0.2333P
\]

Thus, the total amount A received is:
\[
\text{Total Amount A Received} = 0.1333P + 0.2333P = 0.3666P
\]

### 3. Equating A's Total to Rs. 11,000:
We are told that A received a total of Rs. 11,000. So, we set up the equation:
\[
0.3666P = 11
\]
Solving for \( P \) (total profit in thousands of rupees):
\[
P = \frac{11}{0.3666} \approx 30
\]

### 4. Conclusion:
The total profit for the year is approximately **Rs. 30,000**.

Would you like further clarification on any part of the solution?

### Related Questions:
1. How would the solution change if A's salary percentage was different?
2. What if B's salary was 20% of the total profit instead of 16.67%?
3. How much would B receive if the total profit was Rs. 40,000?
4. How is the profit-sharing ratio important in such problems?
5. What would happen if there was a third partner involved?

### Tip:
When solving profit-sharing problems, clearly separate the fixed salary portions from the proportional profit-sharing portions to avoid confusion.

Solve a business profit distribution problem where A and B receive individual salaries and share the remaining profit. Learn how to calculate total profit using percentage-based salaries and a profit-sharing ratio of 1:2. Suitable for students in Grades 9-11.

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