Rs 1980 is 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 B's part is

Options

A. Rs 540
B. Rs 660
C. Rs 1,080
D. Rs 360

Answer

To solve the problem, we need to find B's part when Rs 1980 is divided among A, B, and C under certain conditions. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understand the Problem**: We know that half of A's part, one-third of B's part, and one-sixth of C's part are all equal. We denote A's part as \( A \), B's part as \( B \), and C's part as \( C \).

2. **Set Up the Equations**: From the problem statement, we can write the following equations based on the given conditions:
\[ \frac{A}{2} = \frac{B}{3} = \frac{C}{6} \]

3. **Express A, B, and C in Terms of a Common Variable**: Let’s denote the common value as \( k \). Therefore, we can express A, B, and C as:
\[ A = 2k, \quad B = 3k, \quad C = 6k \]

4. **Sum of Parts**: The total amount distributed among A, B, and C is Rs 1980. Thus, we can write:
\[ A + B + C = 1980 \]
Substituting the expressions for A, B, and C:
\[ 2k + 3k + 6k = 1980 \]

5. **Combine Like Terms**: Combine the terms on the left side:
\[ 11k = 1980 \]

6. **Solve for k**: Divide both sides by 11 to find \( k \):
\[ k = \frac{1980}{11} = 180 \]

7. **Find B's Part**: Now that we have \( k \), we can find B's part:
\[ B = 3k = 3 \times 180 = 540 \]

### Final Answer:
B's part is Rs 540.

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