If 4A=5B and 3A=2C, the ratio fo B:C is

Options

A. 0.16875
B. 0.21388888888889
C. 0.34375
D. 0.42708333333333

Answer

To solve the problem, we need to find the ratio of B to C given the equations \(4A = 5B\) and \(3A = 2C\).

### Step-by-Step Solution:

1. **Start with the given equations**:
\[ 4A = 5B \quad \text{(1)} \]
\[ 3A = 2C \quad \text{(2)} \]

2. **Express A in terms of B from equation (1)**:
\[ A = \frac{5B}{4} \quad \text{(3)} \]

3. **Substitute equation (3) into equation (2)**:
Replace \(A\) in equation (2) with the expression from equation (3):
\[ 3\left(\frac{5B}{4}\right) = 2C \]

4. **Simplify the equation**:
\[ \frac{15B}{4} = 2C \]

5. **Cross-multiply to eliminate the fraction**:
\[ 15B = 8C \quad \text{(4)} \]

6. **Rearrange equation (4) to find the ratio of B to C**:
\[ \frac{B}{C} = \frac{8}{15} \]

7. **Thus, the ratio of B to C is**:
\[ B : C = 8 : 15 \]

### Final Answer:
The ratio of B to C is \(8 : 15\).

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