R and S started a business by investing Rs 165000 and Rs 195000 respectively for the same period of time. If R’s share in the profit earned by them is Rs 11000, then what is the total profit (in Rs) earned by both of them together?

Options

A. 22000
B. 40000
C. 26000
D. 24000

Answer

To solve the problem, we need to determine the total profit earned by R and S based on their investments and R's share of the profit.

### Step-by-Step Solution:

1. **Identify the Investments**:
- R's investment = Rs 165,000
- S's investment = Rs 195,000

2. **Calculate the Total Investment**:
\[ \text{Total Investment} = R's \, investment + S's \, investment = 165000 + 195000 = 360000 \]

3. **Calculate the Profit Sharing Ratio**:
- The profit sharing ratio is based on their investments.
- R's share of the investment = Rs 165,000
- S's share of the investment = Rs 195,000
- The ratio of their investments (R:S) can be calculated as:
\[ R:S = 165000:195000 \]
- Simplifying this ratio:
\[ R:S = 165:195 = 11:13 \quad (\text{by dividing both by 15,000}) \]

4. **Determine R's Share of the Profit**:
- We know R's share in the profit is Rs 11,000.
- Let the total profit be \( P \).
- R's share of the profit can also be expressed in terms of the total profit:
\[ R's \, share = \frac{11}{24} \times P \]
- This is because the total parts in the ratio (11 + 13) = 24.

5. **Set Up the Equation**:
- Since R's share is Rs 11,000, we can set up the equation:
\[ \frac{11}{24} \times P = 11000 \]

6. **Solve for Total Profit \( P \)**:
- To find \( P \), we can rearrange the equation:
\[ P = 11000 \times \frac{24}{11} \]
- Calculating \( P \):
\[ P = 11000 \times 2.1818 \approx 24000 \]

7. **Conclusion**:
- The total profit earned by both R and S together is Rs 24,000.

### Final Answer:
The total profit earned by both R and S together is **Rs 24,000**.