What is R's share on profit a joint venture ?
(i) Q started business investing Rs. 80,000.
(ii) R joined him after 3 months.
(iii) P joined after 4 months with a capital of Rs. 120000 and got Rs. 6000 share of profit.

Options

A. A) (i) and (ii) only
B. B) (ii) and (iii) only
C. C) All (i), (ii), and (iii)
D. D) Even not with all (i), (ii) and (iii) together

Answer

To determine R's share of profit in the joint venture, we need to analyze the information provided in the statements and calculate the profit-sharing ratio based on the capital invested and the time for which it was invested.

### Step-by-Step Solution:

1. **Identify the Investments and Time Periods**:
- Q started the business with an investment of Rs. 80,000 and invested for 12 months.
- R joined after 3 months, meaning R invested for 9 months (12 - 3 = 9).
- P joined after 4 months with an investment of Rs. 120,000 and invested for 8 months (12 - 4 = 8).

2. **Calculate the Capital Contribution**:
- For Q:
\[ \text{Capital Contribution} = 80,000 \times 12 = 960,000 \]
- For R:
\[ \text{Capital Contribution} = R \times 9 \quad \text{(We need to find R's capital)} \]
- For P:
\[ \text{Capital Contribution} = 120,000 \times 8 = 960,000 \]

3. **Set Up the Profit Sharing Ratio**:
- The profit-sharing ratio is based on the total capital contributions:
\[ \text{Total Capital Contribution} = 960,000 + (R \times 9) + 960,000 \]
- The profit-sharing ratio can be expressed as:
\[ \text{Ratio} = \text{Q's Contribution} : \text{R's Contribution} : \text{P's Contribution} = 960,000 : (R \times 9) : 960,000 \]

4. **Use P's Profit Share to Find R's Contribution**:
- We know that P's share of the profit is Rs. 6,000.
- The total profit can be expressed in terms of the ratio:
\[ \text{Total Profit} = \text{Q's Share} + \text{R's Share} + 6,000 \]
- Since P's contribution is equal to Q's contribution, we can find the total profit by setting up the equation based on the ratio.

5. **Conclusion**:
- Without knowing R's capital, we cannot determine R's exact share of the profit. Therefore, we conclude that we need additional information about R's capital investment to calculate R's share accurately.