Amit and Sudesh have invested in the ratio of 4 :7 . If both inversted a total amount of 49500, then find the investment of Sudesh.

Options

A. X 31500
B. X 1800
C. X 31000
D. X 18500

Answer

To solve the problem, we need to find Sudesh's investment based on the ratio of their investments and the total amount they invested together.

### Step-by-Step Solution:

1. **Understand the Ratio**:
Amit and Sudesh have invested in the ratio of 4:7. This means for every 4 parts Amit invests, Sudesh invests 7 parts.

2. **Define Variables**:
Let Amit's investment be represented as \( 4x \) and Sudesh's investment as \( 7x \), where \( x \) is a common multiplier.

3. **Set Up the Equation**:
The total investment made by both Amit and Sudesh is given as 49500. Therefore, we can write the equation:
\[ 4x + 7x = 49500 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 11x = 49500 \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides of the equation by 11:
\[ x = \frac{49500}{11} = 4500 \]

6. **Calculate Sudesh's Investment**:
Now that we have \( x \), we can find Sudesh's investment:
\[ \text{Sudesh's investment} = 7x = 7 \times 4500 = 31500 \]

7. **Conclusion**:
Therefore, Sudesh's investment is \( 31500 \).

### Final Answer:
Sudesh's investment is **31500**.

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