Divide ₹ 715 among A, B, C in such a way that B gets three times as much as A gets and C gets half of as much as B gets .

Answer

To solve the problem of dividing ₹ 715 among A, B, and C based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let A's share be represented as \( X \). According to the problem:
- B gets three times as much as A, so B's share will be \( 3X \).
- C gets half of what B gets, so C's share will be \( \frac{3X}{2} \).

2. **Set Up the Equation**:
The total amount distributed among A, B, and C is ₹ 715. Therefore, we can write the equation:
\[ A + B + C = 715 \]
Substituting the values we defined:
\[ X + 3X + \frac{3X}{2} = 715 \]

3. **Combine Like Terms**:
To combine the terms, we need a common denominator. The common denominator for \( X \), \( 3X \), and \( \frac{3X}{2} \) is 2. Rewriting the equation:
\[ \frac{2X}{2} + \frac{6X}{2} + \frac{3X}{2} = 715 \]
This simplifies to:
\[ \frac{2X + 6X + 3X}{2} = 715 \]
\[ \frac{11X}{2} = 715 \]

4. **Solve for X**:
To eliminate the fraction, multiply both sides by 2:
\[ 11X = 715 \times 2 \]
\[ 11X = 1430 \]
Now, divide both sides by 11:
\[ X = \frac{1430}{11} = 130 \]

5. **Calculate Individual Shares**:
Now that we have \( X \):
- A's share: \( A = X = 130 \)
- B's share: \( B = 3X = 3 \times 130 = 390 \)
- C's share: \( C = \frac{3X}{2} = \frac{3 \times 130}{2} = 195 \)

6. **Final Shares**:
Thus, the final amounts are:
- A gets ₹ 130
- B gets ₹ 390
- C gets ₹ 195

### Summary of Shares:
- A: ₹ 130
- B: ₹ 390
- C: ₹ 195