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 where 10% of m is equal to 20% of n, we can follow these steps:

### Step 1: Set up the equation
We start with the equation based on the information given in the problem:
\[ 10\% \text{ of } m = 20\% \text{ of } n \]
This can be written mathematically as:
\[ \frac{10}{100} \cdot m = \frac{20}{100} \cdot n \]

### Step 2: Simplify the percentages
We can simplify the fractions:
\[ \frac{1}{10} m = \frac{1}{5} n \]

### Step 3: Cross-multiply to eliminate the fractions
To eliminate the fractions, we can cross-multiply:
\[ 1 \cdot n = 2 \cdot m \]
This gives us:
\[ n = 2m \]

### Step 4: Find the ratio of m to n
Now we can express the ratio of m to n. Since \( n = 2m \), we can write:
\[ \frac{m}{n} = \frac{m}{2m} \]
This simplifies to:
\[ \frac{m}{n} = \frac{1}{2} \]

### Step 5: Write the ratio in the form m:n
To express this in the form of m:n, we can write:
\[ m:n = 1:2 \]

### Final Answer
Thus, the ratio of m to n is:
\[ m:n = 1:2 \]

---