Which of the following represents a correct proportion ?

Options

A. `12 : 9 = 16 : 12`
B. `13 : 11 = 5 : 4`
C. `30 : 45 = 13 : 24`
D. `3 : 5 = 2 : 5`

Answer

To determine which of the given options represents a correct proportion, we need to simplify the ratios in each option and check if they are equal. A proportion is established when two ratios are equal.

### Step-by-Step Solution:

1. **Analyze Option 1:**
- The first ratio is \( \frac{12}{9} \).
- Simplifying \( \frac{12}{9} \):
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
- \( \frac{12 \div 3}{9 \div 3} = \frac{4}{3} \).
- The second ratio is \( \frac{16}{12} \).
- Simplifying \( \frac{16}{12} \):
- Divide both the numerator and the denominator by their GCD, which is 4.
- \( \frac{16 \div 4}{12 \div 4} = \frac{4}{3} \).
- Since both simplified ratios are equal (\( \frac{4}{3} = \frac{4}{3} \)), Option 1 represents a correct proportion.

2. **Analyze Option 2:**
- The first ratio is \( \frac{13}{11} \).
- This ratio cannot be simplified further, so it remains \( \frac{13}{11} \).
- The second ratio is \( \frac{5}{4} \).
- This ratio also cannot be simplified further, so it remains \( \frac{5}{4} \).
- Since \( \frac{13}{11} \neq \frac{5}{4} \), Option 2 does not represent a correct proportion.

3. **Analyze Option 3:**
- The first ratio is \( \frac{30}{45} \).
- Simplifying \( \frac{30}{45} \):
- Divide both the numerator and the denominator by their GCD, which is 15.
- \( \frac{30 \div 15}{45 \div 15} = \frac{2}{3} \).
- The second ratio is \( \frac{13}{24} \).
- This ratio cannot be simplified further, so it remains \( \frac{13}{24} \).
- Since \( \frac{2}{3} \neq \frac{13}{24} \), Option 3 does not represent a correct proportion.

4. **Analyze Option 4:**
- The first ratio is \( \frac{3}{5} \).
- This ratio cannot be simplified further, so it remains \( \frac{3}{5} \).
- The second ratio is \( \frac{2}{5} \).
- This ratio also cannot be simplified further, so it remains \( \frac{2}{5} \).
- Since \( \frac{3}{5} \neq \frac{2}{5} \), Option 4 does not represent a correct proportion.

### Conclusion:
The only option that represents a correct proportion is **Option 1**.