Manoj got Rs. 6000 as his share out of a total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs. 20000 for 6 months where as Ramesh invested his amount for the whole year, what was the amount invested by Ramesh?

Options

A. Rs 30000
B. Rs 40000
C. Rs 10000
D. Rs 5000

Answer

To find out the amount invested by Ramesh, we can use the concept of profit-sharing in partnerships, which is based on the amount of capital invested and the time for which it is invested.

### Step-by-Step Solution:

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

2. **Investment Details**:
- Manoj invested Rs. 20000 for 6 months.
- Let Ramesh's investment be Rs. R for 12 months (1 year).

3. **Calculate the Effective Investment**:
- Manoj's effective investment = Amount invested × Time = 20000 × 6 = 120000
- Ramesh's effective investment = Amount invested × Time = R × 12

4. **Set Up the Ratio of Profits**:
- The ratio of profits is equal to the ratio of their effective investments.
- Therefore, we can set up the equation:
\[ \frac{Manoj's\ effective\ investment}{Ramesh's\ effective\ investment} = \frac{6000}{3000} \]
- Simplifying the right side gives:
\[ \frac{Manoj's\ effective\ investment}{Ramesh's\ effective\ investment} = 2 \]

5. **Substituting the Effective Investments**:
- Substitute the effective investments into the ratio:
\[ \frac{120000}{R \times 12} = 2 \]

6. **Cross-Multiply to Solve for R**:
- Cross-multiplying gives:
\[ 120000 = 2 \times R \times 12 \]
- Simplifying this gives:
\[ 120000 = 24R \]

7. **Solve for R**:
- Divide both sides by 24:
\[ R = \frac{120000}{24} = 5000 \]

Therefore, Ramesh invested **Rs. 5000**.