If 10% of m is the same as 20% of n, then m : n is equal to :

Options

A. `2:1`
B. `1:2`
C. `1:10`
D. `1 : 20`

Answer

To solve the problem, we need to establish the relationship between \( m \) and \( n \) based on the given percentages.

### Step-by-Step Solution:

1. **Set Up the Equation**:
We know that 10% of \( m \) is equal to 20% of \( n \). This can be expressed mathematically as:
\[ 0.1m = 0.2n \]

2. **Eliminate Decimals**:
To simplify the equation, we can multiply both sides by 100 to eliminate the decimals:
\[ 10m = 20n \]

3. **Rearrange the Equation**:
Next, we can rearrange the equation to isolate \( m \) in terms of \( n \):
\[ m = \frac{20n}{10} \]

4. **Simplify the Expression**:
Simplifying the right side gives us:
\[ m = 2n \]

5. **Express the Ratio**:
Now, we can express the ratio \( m:n \):
\[ m:n = 2n:n \]

6. **Simplify the Ratio**:
This simplifies to:
\[ m:n = 2:1 \]

### Final Answer:
Thus, the ratio \( m:n \) is equal to \( 2:1 \).

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