Which of the following is equivalent to `7:8` ?

Options

A. `142: 128`
B. `112: 124`
C. `136: 116`
D. `119: 136`

Answer

To determine which of the given ratios is equivalent to \(7:8\), we will simplify each option and compare it to \(7:8\).

### Step-by-Step Solution:

1. **Identify the Ratios**: We are given four options. Let's denote them as:
- Option 1: \(142:128\)
- Option 2: \(112:124\)
- Option 3: \(136:116\)
- Option 4: \(119:136\)

2. **Convert Ratios to Fractions**: Convert each ratio to a fraction for easier simplification.
- Option 1: \(\frac{142}{128}\)
- Option 2: \(\frac{112}{124}\)
- Option 3: \(\frac{136}{116}\)
- Option 4: \(\frac{119}{136}\)

3. **Simplify Each Fraction**:
- **Option 1**:
\[ \frac{142}{128} = \frac{71}{64} \quad \text{(dividing both by 2)} \]
- **Option 2**:
\[ \frac{112}{124} = \frac{28}{31} \quad \text{(dividing both by 4)} \]
- **Option 3**:
\[ \frac{136}{116} = \frac{34}{29} \quad \text{(dividing both by 4)} \]
- **Option 4**:
\[ \frac{119}{136} = \frac{7}{8} \quad \text{(dividing both by 17)} \]

4. **Compare with \(7:8\)**: Now we compare each simplified fraction with \(\frac{7}{8}\):
- Option 1: \(\frac{71}{64}\) is not equal to \(\frac{7}{8}\).
- Option 2: \(\frac{28}{31}\) is not equal to \(\frac{7}{8}\).
- Option 3: \(\frac{34}{29}\) is not equal to \(\frac{7}{8}\).
- Option 4: \(\frac{7}{8}\) is equal to \(\frac{7}{8}\).

5. **Conclusion**: The fourth option \(119:136\) is equivalent to \(7:8\).

### Final Answer:
The ratio equivalent to \(7:8\) is **Option 4: \(119:136\)**.