When rupes 4572 is divided among A,B and C such that three times of A's share is equal to 4 times of B's share is equal 6 times C's share. What is A's share ?

Answer

To solve the problem of dividing Rupees 4572 among A, B, and C based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem Statement**:
We need to divide Rupees 4572 among A, B, and C such that:
- 3 times A's share = 4 times B's share = 6 times C's share.

2. **Set Up the Ratios**:
Let A's share be \( A \), B's share be \( B \), and C's share be \( C \).
From the problem, we can write:
\[ 3A = 4B = 6C \]

3. **Express A, B, and C in Terms of a Common Variable**:
We can express A, B, and C in terms of a common variable \( x \):
- From \( 3A = 4B \), we get \( A = \frac{4}{3}B \).
- From \( 3A = 6C \), we get \( A = 2C \).

Now, let's express B and C in terms of A:
- From \( A = \frac{4}{3}B \), we can express \( B \) as:
\[ B = \frac{3}{4}A \]
- From \( A = 2C \), we can express \( C \) as:
\[ C = \frac{1}{2}A \]

4. **Form the Ratio**:
Now we can express the shares in terms of a single variable:
- Let \( A = 4x \)
- Then \( B = 3x \)
- And \( C = 2x \)

Thus, the ratio of A, B, and C is:
\[ A : B : C = 4x : 3x : 2x \]

5. **Find the Total Parts**:
The total parts of the shares can be calculated as:
\[ 4x + 3x + 2x = 9x \]

6. **Set Up the Equation with Total Amount**:
We know that the total amount is Rupees 4572:
\[ 9x = 4572 \]

7. **Solve for x**:
To find \( x \), divide both sides by 9:
\[ x = \frac{4572}{9} = 508 \]

8. **Calculate A's Share**:
Now, we can find A's share:
\[ A = 4x = 4 \times 508 = 2032 \]

### Final Answer:
A's share is **Rupees 2032**.

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