If 10% of x = 20% of y, then x: y is equal to :

Options

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

Answer

To solve the problem where 10% of x is equal to 20% of y, we can follow these steps:

### Step 1: Set up the equation
We start by translating the percentages into equations. We know that:
\[ 10\% \text{ of } x = 20\% \text{ of } y \]
This can be written mathematically as:
\[ \frac{10}{100} \cdot x = \frac{20}{100} \cdot y \]

### Step 2: Simplify the equation
Now, we simplify both sides of the equation:
\[ \frac{1}{10} x = \frac{1}{5} y \]

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

### Step 4: Express x in terms of y
We can rearrange the equation to express x in terms of y:
\[ \frac{x}{y} = \frac{1}{2} \]

### Step 5: Find the ratio x:y
To find the ratio of x to y, we can write:
\[ x : y = 1 : 2 \]

### Step 6: Write the final answer
The final answer for the ratio of x to y is:
\[ x : y = 2 : 1 \]