Rs. 2780 are invested party in `4%` stok at 75 and `5%` stock at 80 to have equal amount of incomes . The investment in `5%` stock is

Options

A. Rs 1500
B. Rs 1280
C. Rs 1434.84
D. Rs 1640

Answer

To solve the problem, we need to find out how much is invested in the 5% stock given that the total investment is Rs. 2780 and the incomes from both stocks are equal.

### Step-by-Step Solution:

1. **Let the Investment in 4% Stock be \( n \)**:
- We denote the amount invested in the 4% stock as \( n \).
- Therefore, the investment in the 5% stock will be \( 2780 - n \).

2. **Calculate the Income from 4% Stock**:
- The income from the 4% stock can be calculated using the formula:
\[ \text{Income from 4% Stock} = \frac{4}{100} \times n \div \frac{75}{100} = \frac{4n}{75} \]

3. **Calculate the Income from 5% Stock**:
- The income from the 5% stock can be calculated as:
\[ \text{Income from 5% Stock} = \frac{5}{100} \times (2780 - n) \div \frac{80}{100} = \frac{5(2780 - n)}{80} \]

4. **Set the Incomes Equal**:
- According to the problem, the incomes from both stocks are equal:
\[ \frac{4n}{75} = \frac{5(2780 - n)}{80} \]

5. **Cross-Multiply to Solve for \( n \)**:
- Cross-multiplying gives us:
\[ 4n \times 80 = 5(2780 - n) \times 75 \]
- Simplifying this:
\[ 320n = 5 \times 75 \times 2780 - 375n \]
- Combine like terms:
\[ 320n + 375n = 5 \times 75 \times 2780 \]
\[ 695n = 5 \times 75 \times 2780 \]

6. **Calculate \( n \)**:
- First, calculate \( 5 \times 75 \times 2780 \):
\[ 5 \times 75 = 375 \]
\[ 375 \times 2780 = 1042500 \]
- Now, solve for \( n \):
\[ n = \frac{1042500}{695} \approx 1500 \]

7. **Find the Investment in 5% Stock**:
- Now that we have \( n \), we can find the investment in the 5% stock:
\[ \text{Investment in 5% Stock} = 2780 - n = 2780 - 1500 = 1280 \]

### Final Answer:
The investment in the 5% stock is **Rs. 1280**.