if 3 kg 500g : 7 kg : : 27 kg : m kg, then m = _____

Options

A. 36
B. 360
C. 540
D. 54

Explanation

To solve the problem, we need to find the value of \( m \) in the ratio \( 3 \, \text{kg} \, 500 \, \text{g} : 7 \, \text{kg} :: 27 \, \text{kg} : m \, \text{kg} \).

### Step-by-Step Solution

1. **Convert all weights to grams**:
- \( 3 \, \text{kg} \, 500 \, \text{g} \) can be converted to grams:
\[ 3 \, \text{kg} = 3 \times 1000 \, \text{g} = 3000 \, \text{g} \]
\[ 3 \, \text{kg} \, 500 \, \text{g} = 3000 \, \text{g} + 500 \, \text{g} = 3500 \, \text{g} \]
- \( 7 \, \text{kg} \) can be converted to grams:
\[ 7 \, \text{kg} = 7 \times 1000 \, \text{g} = 7000 \, \text{g} \]

2. **Set up the ratio**:
- The ratio of \( 3 \, \text{kg} \, 500 \, \text{g} \) to \( 7 \, \text{kg} \) is:
\[ \frac{3500 \, \text{g}}{7000 \, \text{g}} = \frac{1}{2} \]

3. **Set up the proportion**:
- According to the problem, we have:
\[ \frac{1}{2} = \frac{27 \, \text{kg}}{m \, \text{kg}} \]

4. **Cross-multiply to solve for \( m \)**:
- Cross-multiplying gives:
\[ 1 \times m = 2 \times 27 \, \text{kg} \]
\[ m = 54 \, \text{kg} \]

5. **Final answer**:
- Therefore, the value of \( m \) is:
\[ m = 54 \, \text{kg} \]