If `22% of x = 30% of ` y, then y : x is equal to :

Options

A. `15 : 11 `
B. `11:15`
C. `17:16`
D. `15:14`

Answer

To solve the equation \( 22\% \text{ of } x = 30\% \text{ of } y \), we can follow these steps:

### Step 1: Write the equation in terms of x and y
We start with the equation:
\[ 22\% \text{ of } x = 30\% \text{ of } y \]
This can be expressed mathematically as:
\[ \frac{22}{100} \cdot x = \frac{30}{100} \cdot y \]

### Step 2: Eliminate the percentage
To simplify, we can multiply both sides of the equation by 100 to eliminate the percentage:
\[ 22x = 30y \]

### Step 3: Rearrange the equation
Next, we want to express \( y \) in terms of \( x \):
\[ y = \frac{22}{30}x \]

### Step 4: Simplify the fraction
We can simplify the fraction \( \frac{22}{30} \):
\[ y = \frac{11}{15}x \]

### Step 5: Find the ratio y : x
Now, we can express the ratio \( y : x \):
\[ y : x = \frac{11}{15} : 1 \]
This can be written as:
\[ y : x = 11 : 15 \]

### Final Answer
Thus, the ratio \( y : x \) is equal to \( 11 : 15 \).

---