0.6 of a number equals 0.09 of another number the ratio of the number is

Options

A. 2 : 3
B. 1 : 15
C. 20 : 3
D. 3 : 20

Answer

To solve the problem step by step, let's denote the two numbers as \( m \) and \( n \).

### Step 1: Set up the equation
According to the problem, we have:
\[ 0.6m = 0.09n \]

### Step 2: Rearrange the equation to find the ratio
To find the ratio of \( m \) to \( n \), we can rearrange the equation:
\[ \frac{m}{n} = \frac{0.09}{0.6} \]

### Step 3: Simplify the fraction
Now, we need to simplify the fraction \( \frac{0.09}{0.6} \):
1. Convert the decimals to fractions:
- \( 0.09 = \frac{9}{100} \)
- \( 0.6 = \frac{6}{10} = \frac{3}{5} \)

2. Now substitute these fractions into the ratio:
\[ \frac{m}{n} = \frac{\frac{9}{100}}{\frac{3}{5}} \]

3. To divide by a fraction, multiply by its reciprocal:
\[ \frac{m}{n} = \frac{9}{100} \times \frac{5}{3} \]

4. Now multiply the fractions:
\[ \frac{m}{n} = \frac{9 \times 5}{100 \times 3} = \frac{45}{300} \]

### Step 4: Simplify the ratio
Now, simplify \( \frac{45}{300} \):
1. Find the greatest common divisor (GCD) of 45 and 300, which is 15.
2. Divide both the numerator and the denominator by 15:
\[ \frac{45 \div 15}{300 \div 15} = \frac{3}{20} \]

### Final Answer
Thus, the ratio of the two numbers \( m \) and \( n \) is:
\[ \frac{m}{n} = \frac{3}{20} \]