If two numbers are respectively 20% and 50% of a third number, what is the ratio between the two numbers ?

Options

A. `5:2`
B. `2:5`
C. `1:5`
D. `1:2`

Answer

To find the ratio between two numbers that are respectively 20% and 50% of a third number, we can follow these steps:

### Step-by-Step Solution:

1. **Let the third number be \( x \)**:
- We denote the third number as \( x \).

2. **Calculate the first number**:
- The first number is 20% of \( x \).
- This can be calculated as:
\[ \text{First number} = \frac{20}{100} \times x = \frac{1}{5}x \]

3. **Calculate the second number**:
- The second number is 50% of \( x \).
- This can be calculated as:
\[ \text{Second number} = \frac{50}{100} \times x = \frac{1}{2}x \]

4. **Set up the ratio of the two numbers**:
- We need to find the ratio of the first number to the second number:
\[ \text{Ratio} = \frac{\text{First number}}{\text{Second number}} = \frac{\frac{1}{5}x}{\frac{1}{2}x} \]

5. **Simplify the ratio**:
- The \( x \) in the numerator and denominator cancels out:
\[ \text{Ratio} = \frac{\frac{1}{5}}{\frac{1}{2}} = \frac{1}{5} \times \frac{2}{1} = \frac{2}{5} \]

6. **Express the ratio in standard form**:
- The ratio of the two numbers is:
\[ 2:5 \]

### Final Answer:
The ratio between the two numbers is \( 2:5 \).

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