Three persons A, B and C enter into a partnership with the investment ratio is 12:8:9 and the time ratio is 5:4:3. B receive Rs. more profit than C received. Average of the profit amount received by A and C together is Rs.

To solve the problem, let's analyze the partnership step by step.

### Step 1: Determine the profit-sharing ratio.
The profit-sharing ratio in a partnership is calculated by multiplying the investment ratio by the time ratio for each person.

- For A: \( \text{Investment Ratio} = 12 \), \( \text{Time Ratio} = 5 \)
  \[
  \text{A's Share} = 12 \times 5 = 60
  \]
- For B: \( \text{Investment Ratio} = 8 \), \( \text{Time Ratio} = 4 \)
  \[
  \text{B's Share} = 8 \times 4 = 32
  \]
- For C: \( \text{Investment Ratio} = 9 \), \( \text{Time Ratio} = 3 \)
  \[
  \text{C's Share} = 9 \times 3 = 27
  \]

So, the profit-sharing ratio of A, B, and C is \( 60:32:27 \).

### Step 2: Determine the profit difference between B and C.
Let the total profit be \( P \).

- The share of profit for B is:
  \[
  \text{B's Profit} = \frac{32}{60 + 32 + 27} \times P = \frac{32}{119} \times P
  \]
- The share of profit for C is:
  \[
  \text{C's Profit} = \frac{27}{119} \times P
  \]

Given that B receives Rs. \( x \) more than C:
\[
\frac{32}{119} \times P = \frac{27}{119} \times P + x
\]

### Step 3: Calculate the average profit of A and C.
The share of profit for A is:
\[
\text{A's Profit} = \frac{60}{119} \times P
\]

The average profit received by A and C is:
\[
\text{Average Profit} = \frac{\text{A's Profit} + \text{C's Profit}}{2} = \frac{\frac{60}{119} \times P + \frac{27}{119} \times P}{2} = \frac{\frac{87}{119} \times P}{2} = \frac{87}{238} \times P
\]

### Conclusion
The average profit amount received by A and C together is \( \frac{87}{238} \times P \).

Without additional information on the specific value of \( x \) or the total profit \( P \), this is the most detailed expression for the average profit of A and C together.

Do you want more details, or have any questions? 

Here are 5 related questions for practice:
1. If B received Rs. 600 more than C, what was the total profit \( P \)?
2. What is the total profit if A's share is Rs. 9000?
3. If the total profit is Rs. 11900, what is the share of each partner?
4. What is the percentage share of each partner in the total profit?
5. If C's profit is Rs. 5400, how much more did B receive than C?

**Tip:** Always ensure to account for both investment and time when calculating profit shares in partnerships.

Learn how to solve a partnership profit sharing problem involving investment and time ratios. Understand how to calculate individual profit shares and find the average profit of specific partners. Suitable for students in Grades 9-12.

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