Rs 12540/- is divided among A. B and C in such a way that A gets `3/7` part of total amount of B and Cand B gets `2/9` part of total amount of A and C. What is the difference between parts of A and B?

Options

A. Rs 1482
B. Rs 2736
C. Rs 4218
D. Rs 4320

Answer

To solve the problem, we need to find the difference between the amounts received by A and B when Rs 12,540 is divided among A, B, and C based on the given conditions.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- We have a total amount of Rs 12,540.
- A receives \( \frac{3}{7} \) of the total amount of B and C.
- B receives \( \frac{2}{9} \) of the total amount of A and C.

2. **Setting Up the Equations:**
- Let the amounts received by A, B, and C be denoted as \( a \), \( b \), and \( c \) respectively.
- According to the problem:
\[ a = \frac{3}{7}(b + c) \]
\[ b = \frac{2}{9}(a + c) \]

3. **Expressing \( b + c \) and \( a + c \):**
- From the first equation, we can express \( b + c \) in terms of \( a \):
\[ b + c = \frac{7}{3}a \]
- From the second equation, we can express \( a + c \) in terms of \( b \):
\[ a + c = \frac{9}{2}b \]

4. **Substituting \( b + c \) and \( a + c \) into the Total Amount:**
- We know:
\[ a + b + c = 12,540 \]
- We can express \( c \) in terms of \( a \) and \( b \):
\[ c = 12,540 - a - b \]

5. **Using the Equations:**
- Substitute \( b + c \) into the total amount equation:
\[ a + \left(\frac{7}{3}a - c\right) + c = 12,540 \]
- Rearranging gives us:
\[ a + \frac{7}{3}a = 12,540 \]
- Combine like terms:
\[ \frac{10}{3}a = 12,540 \]
- Solving for \( a \):
\[ a = \frac{12,540 \times 3}{10} = 3,762 \]

6. **Finding \( b \):**
- Now substitute \( a \) back into the equation for \( b \):
\[ b = \frac{2}{9}(3,762 + c) \]
- We can find \( c \) using \( b + c = \frac{7}{3}a \):
\[ b + c = \frac{7}{3}(3,762) = 8,804 \]
- Now we can express \( c \) in terms of \( b \):
\[ c = 8,804 - b \]

7. **Solving for \( b \) and \( c \):**
- Substitute \( c \) back into the equation for \( b \):
\[ b = \frac{2}{9}(3,762 + (8,804 - b)) \]
- Solving this will give us the value of \( b \).

8. **Finding the Difference:**
- Finally, the difference between \( a \) and \( b \) is:
\[ \text{Difference} = a - b \]