What will be the dublicate ratio of 5:9?

Options

A. a. 10:18
B. b. 20:36
C. c. 25:81
D. d. none of these

Answer

To find the duplicate ratio of 5:9, we follow these steps:

### Step-by-Step Solution:

1. **Understanding Duplicate Ratio**:
The duplicate ratio of two numbers \( a:b \) is defined as the square of the ratio. Therefore, the duplicate ratio of \( 5:9 \) can be expressed mathematically as:
\[ \text{Duplicate Ratio} = \left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2} \]

2. **Applying the Formula**:
For the given ratio \( 5:9 \):
\[ \text{Duplicate Ratio} = \left(\frac{5}{9}\right)^2 \]

3. **Calculating the Squares**:
Now, we calculate the squares of the numerator and denominator:
\[ 5^2 = 25 \quad \text{and} \quad 9^2 = 81 \]

4. **Forming the Duplicate Ratio**:
Substitute the squared values back into the ratio:
\[ \text{Duplicate Ratio} = \frac{25}{81} \]

5. **Final Answer**:
Therefore, the duplicate ratio of \( 5:9 \) is:
\[ 25:81 \]