Two friends Pinki and Rinki entered into a partnership by investing an amount of Rs 6000 and Rs 9000 respectively and ratio of their period of investment is `2:3`.Find the profit share of Pinki if profit share of Rinki is Rs 45,000

Options

A. A)Rs 24,000
B. B)Rs 20,000
C. C)Rs 18,000
D. D)Rs 28,000

Answer

To solve the problem, we need to determine Pinki's profit share based on the information provided about their investments and the ratio of their investment periods.

### Step-by-Step Solution:

1. **Identify the Investments:**
- Pinki's investment = Rs 6000
- Rinki's investment = Rs 9000

2. **Calculate the Ratio of Investments:**
- The ratio of their investments can be simplified:
\[ \text{Investment Ratio} = \frac{6000}{9000} = \frac{2}{3} \]

3. **Identify the Ratio of Investment Periods:**
- The ratio of their investment periods is given as 2:3.

4. **Calculate the Overall Profit Ratio:**
- To find the overall profit ratio, we multiply the investment ratio by the time ratio.
- For Pinki:
\[ \text{Pinki's Contribution} = 6000 \times 2 = 12000 \]
- For Rinki:
\[ \text{Rinki's Contribution} = 9000 \times 3 = 27000 \]
- Therefore, the overall profit ratio is:
\[ \text{Overall Profit Ratio} = 12000 : 27000 = 4 : 9 \]

5. **Given Rinki's Profit Share:**
- Rinki's profit share is given as Rs 45000.

6. **Determine the Value of Each Part:**
- Since the ratio of their profits is 4:9, we can set up the equation:
\[ 9x = 45000 \implies x = \frac{45000}{9} = 5000 \]

7. **Calculate Pinki's Profit Share:**
- Now, we can find Pinki's profit share using the ratio:
\[ \text{Pinki's Profit Share} = 4x = 4 \times 5000 = 20000 \]

8. **Final Answer:**
- Pinki's profit share is Rs 20000.