Rs. 3960 are divided among A, B and C so that half of A's part, one -third of B's part and one sixth of C's part are equal. Then C's part is

Options

A. 720
B. 2160
C. 1080
D. 810

Answer

To solve the problem of dividing Rs. 3960 among A, B, and C such that half of A's part, one-third of B's part, and one-sixth of C's part are equal, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Parts**:
Let A's part be \( A \), B's part be \( B \), and C's part be \( C \).

2. **Set Up the Equation**:
According to the problem, we have:
\[ \frac{A}{2} = \frac{B}{3} = \frac{C}{6} \]
Let's denote this common value as \( k \). Therefore, we can express A, B, and C in terms of \( k \):
\[ A = 2k, \quad B = 3k, \quad C = 6k \]

3. **Sum of Parts**:
The total amount distributed among A, B, and C is Rs. 3960. Hence, we can write:
\[ A + B + C = 3960 \]
Substituting the expressions for A, B, and C:
\[ 2k + 3k + 6k = 3960 \]

4. **Combine Like Terms**:
Combine the terms on the left:
\[ 11k = 3960 \]

5. **Solve for k**:
Now, divide both sides by 11 to find \( k \):
\[ k = \frac{3960}{11} = 360 \]

6. **Find Individual Parts**:
Now that we have \( k \), we can find A, B, and C:
\[ A = 2k = 2 \times 360 = 720 \]
\[ B = 3k = 3 \times 360 = 1080 \]
\[ C = 6k = 6 \times 360 = 2160 \]

7. **Conclusion**:
Therefore, C's part is:
\[ C = 2160 \]

### Final Answer:
C's part is Rs. 2160.

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