What will be the duplicate ratio of 2 : 7?

Options

A. `4:49`
B. `49 : 4`
C. `4 : 14`
D. `8 ,23`

Answer

To find the duplicate ratio of 2 : 7, we follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Duplicate Ratio**:
The duplicate ratio of a ratio \( a : b \) is obtained by squaring both the terms of the ratio.

2. **Identify the Given Ratio**:
Here, the given ratio is \( 2 : 7 \).

3. **Square the Numerator**:
We take the numerator (which is 2) and square it:
\[ 2^2 = 4 \]

4. **Square the Denominator**:
Next, we take the denominator (which is 7) and square it:
\[ 7^2 = 49 \]

5. **Form the Duplicate Ratio**:
Now, we combine the squared values to form the duplicate ratio:
\[ \text{Duplicate Ratio} = 4 : 49 \]

### Final Answer:
The duplicate ratio of \( 2 : 7 \) is \( 4 : 49 \).

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