Divide ₹ 760 among A, B, C such that A gets `(5)/(6)` of what B gets and the ratio between the shares of B and C is 3 : 4

Answer

To solve the problem of dividing ₹760 among A, B, and C based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
Let the amount received by B be represented as \( 3x \). Since the ratio of B to C is 3:4, we can express the amount received by C as \( 4x \).

2. **Calculate A's Share:**
According to the problem, A receives \( \frac{5}{6} \) of what B receives. Therefore, A's share can be calculated as:
\[ A = \frac{5}{6} \times (3x) = \frac{15x}{6} = \frac{5x}{2} \]

3. **Set Up the Equation:**
The total amount distributed among A, B, and C is ₹760. Thus, we can write the equation:
\[ A + B + C = 760 \]
Substituting the values we have:
\[ \frac{5x}{2} + 3x + 4x = 760 \]

4. **Combine Like Terms:**
To combine the terms, we first convert \( 3x \) and \( 4x \) into fractions with a common denominator:
\[ \frac{5x}{2} + \frac{6x}{2} + \frac{8x}{2} = 760 \]
This simplifies to:
\[ \frac{19x}{2} = 760 \]

5. **Solve for x:**
To eliminate the fraction, multiply both sides by 2:
\[ 19x = 1520 \]
Now, divide both sides by 19:
\[ x = \frac{1520}{19} = 80 \]

6. **Calculate Individual Shares:**
- **A's Share:**
\[ A = \frac{5x}{2} = \frac{5 \times 80}{2} = 200 \]
- **B's Share:**
\[ B = 3x = 3 \times 80 = 240 \]
- **C's Share:**
\[ C = 4x = 4 \times 80 = 320 \]

7. **Final Shares:**
- A receives ₹200
- B receives ₹240
- C receives ₹320

8. **Verify the Total:**
To ensure our solution is correct, we can add the shares:
\[ 200 + 240 + 320 = 760 \]

### Final Answer:
- A's Share: ₹200
- B's Share: ₹240
- C's Share: ₹320