Which of the following are not in proportion?

Options

A. `7: 12 and 805:1380`
B. `16:28 and 4:7`
C. `150:100 and 135:90`
D. `51 :85 and 57:98`

Answer

To determine which of the given ratios are not in proportion, we will follow these steps:

### Step 1: Understand the Concept of Proportion
Two ratios \( \frac{A}{B} \) and \( \frac{C}{D} \) are in proportion if \( A \times D = B \times C \). If this equality holds, then the ratios are in proportion; otherwise, they are not.

### Step 2: Check Each Option
We will check each pair of ratios provided in the options.

#### Option 1: \( \frac{7}{12} \) and \( \frac{805}{1380} \)
1. Calculate \( 7 \times 1380 \) and \( 12 \times 805 \).
- \( 7 \times 1380 = 9660 \)
- \( 12 \times 805 = 9660 \)
2. Since \( 9660 = 9660 \), these ratios are in proportion.

#### Option 2: \( \frac{16}{28} \) and \( \frac{4}{7} \)
1. Calculate \( 16 \times 7 \) and \( 28 \times 4 \).
- \( 16 \times 7 = 112 \)
- \( 28 \times 4 = 112 \)
2. Since \( 112 = 112 \), these ratios are in proportion.

#### Option 3: \( \frac{150}{100} \) and \( \frac{135}{90} \)
1. Calculate \( 150 \times 90 \) and \( 100 \times 135 \).
- \( 150 \times 90 = 13500 \)
- \( 100 \times 135 = 13500 \)
2. Since \( 13500 = 13500 \), these ratios are in proportion.

#### Option 4: \( \frac{51}{85} \) and \( \frac{57}{98} \)
1. Calculate \( 51 \times 98 \) and \( 85 \times 57 \).
- \( 51 \times 98 = 4998 \)
- \( 85 \times 57 = 4845 \)
2. Since \( 4998 \neq 4845 \), these ratios are not in proportion.

### Conclusion
The ratios that are not in proportion are from Option 4: \( \frac{51}{85} \) and \( \frac{57}{98} \).

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