A,B,C are three partners in a business.if twice the investment of A is equal to thrice the capital of B and the capital of B is four times the capital of C.Out of a total profit of Rs.5940 the share of C is

Options

A. Rs 700
B. Rs 900
C. Rs 740
D. Rs 540

Answer

To solve the problem, we need to establish the relationships between the investments of partners A, B, and C based on the information provided.

### Step-by-Step Solution:

1. **Establish Relationships**:
- Let the capital of C be \( x \).
- According to the problem, the capital of B is four times the capital of C. Therefore, we can express the capital of B as:
\[ B = 4x \]
- It is also given that twice the investment of A is equal to thrice the capital of B. We can express this relationship as:
\[ 2A = 3B \]
- Substituting \( B = 4x \) into the equation gives us:
\[ 2A = 3(4x) = 12x \]
- From this, we can find A:
\[ A = \frac{12x}{2} = 6x \]

2. **Summarize Investments**:
- Now we have the investments of A, B, and C:
- \( A = 6x \)
- \( B = 4x \)
- \( C = x \)

3. **Calculate Total Investment**:
- The total investment of all partners is:
\[ \text{Total Investment} = A + B + C = 6x + 4x + x = 11x \]

4. **Determine Profit Sharing**:
- The total profit is given as Rs. 5940. The share of each partner is proportional to their investment. To find C's share, we first determine the fraction of the total investment that C represents:
\[ \text{C's Share} = \frac{C}{\text{Total Investment}} \times \text{Total Profit} \]
- Substituting the values we have:
\[ \text{C's Share} = \frac{x}{11x} \times 5940 = \frac{1}{11} \times 5940 \]

5. **Calculate C's Share**:
- Now we compute C's share:
\[ \text{C's Share} = \frac{5940}{11} = 540 \]

### Final Answer:
C's share of the profit is Rs. 540.