Rs 3,000 is divided between A, B and C, so that A receives `1/3` as much as B and C together receive and B receives `2/3` as much as A and C together receive. Then the share of C is

Options

A. Rs 600
B. Rs 525
C. Rs 1,625
D. Rs 1,050

Answer

To solve the problem, we need to find the shares of A, B, and C from a total of Rs 3000 based on the given conditions.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that:
- A receives \( \frac{1}{3} \) of what B and C together receive.
- B receives \( \frac{2}{3} \) of what A and C together receive.

2. **Setting Up the Equations**:
Let's denote the shares of A, B, and C as \( A \), \( B \), and \( C \) respectively.
- From the first condition:
\[ A = \frac{1}{3}(B + C) \]
- From the second condition:
\[ B = \frac{2}{3}(A + C) \]

3. **Rearranging the Equations**:
We can rearrange the first equation:
\[ 3A = B + C \quad \text{(Equation 1)} \]
Rearranging the second equation gives:
\[ 3B = 2A + 2C \quad \text{(Equation 2)} \]

4. **Expressing C in terms of A and B**:
From Equation 1, we can express \( C \):
\[ C = 3A - B \quad \text{(Substituting into Equation 2)} \]

5. **Substituting C into Equation 2**:
Substitute \( C \) in Equation 2:
\[ 3B = 2A + 2(3A - B) \]
Simplifying this:
\[ 3B = 2A + 6A - 2B \]
\[ 3B + 2B = 8A \]
\[ 5B = 8A \]
Thus, we have:
\[ B = \frac{8}{5}A \quad \text{(Equation 3)} \]

6. **Substituting B back into Equation 1**:
Substitute \( B \) from Equation 3 into Equation 1:
\[ 3A = \frac{8}{5}A + C \]
Rearranging gives:
\[ C = 3A - \frac{8}{5}A \]
\[ C = \frac{15A}{5} - \frac{8A}{5} = \frac{7A}{5} \quad \text{(Equation 4)} \]

7. **Finding A, B, and C in terms of a common variable**:
Now we have:
- \( A = A \)
- \( B = \frac{8}{5}A \)
- \( C = \frac{7}{5}A \)

8. **Finding the total**:
The total amount is:
\[ A + B + C = A + \frac{8}{5}A + \frac{7}{5}A = A + \frac{15A}{5} = A + 3A = 4A \]

9. **Setting the total equal to Rs 3000**:
\[ 4A = 3000 \]
\[ A = \frac{3000}{4} = 750 \]

10. **Finding B and C**:
- From Equation 3:
\[ B = \frac{8}{5} \times 750 = 1200 \]
- From Equation 4:
\[ C = \frac{7}{5} \times 750 = 1050 \]

11. **Conclusion**:
The share of C is Rs 1050.