Sandeep got Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Saketh earned at the end of one year. If Sandeep invested Rs. 20000 for 6 months, whereas Saketh invested his amount for the whole year, the amount invested by Saketh?

Options

A. A) Rs. 5000
B. B) Rs. 6200
C. C) Rs. 8100
D. D) Rs. 7600

Answer

To solve the problem, we need to determine the amount invested by Saketh based on the profit-sharing ratio between Sandeep and Saketh.

### Step-by-Step Solution:

1. **Identify the Profit Shares:**
- Total profit = Rs. 9000
- Sandeep's share = Rs. 6000
- Saketh's share = Total profit - Sandeep's share = 9000 - 6000 = Rs. 3000

2. **Calculate Sandeep's Investment Contribution:**
- Sandeep invested Rs. 20000 for 6 months.
- To find the effective investment (in terms of months), we calculate:
\[ \text{Sandeep's effective investment} = 20000 \times 6 = 120000 \]

3. **Let Saketh's Investment be \( x \):**
- Saketh invested for the whole year (12 months).
- Thus, Saketh's effective investment is:
\[ \text{Saketh's effective investment} = x \times 12 \]

4. **Set Up the Ratio of Investments:**
- The profit is divided according to the ratio of their effective investments:
\[ \frac{\text{Sandeep's effective investment}}{\text{Saketh's effective investment}} = \frac{6000}{3000} \]
- Simplifying the right side gives:
\[ \frac{120000}{x \times 12} = \frac{2}{1} \]

5. **Cross-Multiply to Solve for \( x \):**
- Cross-multiplying gives:
\[ 120000 = 2 \times (x \times 12) \]
- Simplifying further:
\[ 120000 = 24x \]
- Now, divide both sides by 24:
\[ x = \frac{120000}{24} = 5000 \]

6. **Conclusion:**
- The amount invested by Saketh is Rs. 5000.

### Final Answer:
Saketh invested Rs. 5000.