If `50%` of `x=30%` of y then `x : y` is :

Options

A. `5 : 3`
B. `3 : 5`
C. `2 : 3`
D. `3 : 2`

Answer

To solve the problem, we start with the equation given in the question:

1. **Write the equation based on the problem statement:**
\[ 50\% \text{ of } x = 30\% \text{ of } y \]
This can be rewritten in mathematical terms as:
\[ \frac{50}{100} \cdot x = \frac{30}{100} \cdot y \]

2. **Simplify the percentages:**
We can simplify the fractions:
\[ \frac{1}{2} \cdot x = \frac{3}{10} \cdot y \]

3. **Eliminate the fractions by multiplying both sides by 10:**
To eliminate the fractions, we can multiply both sides by 10:
\[ 10 \cdot \left(\frac{1}{2} \cdot x\right) = 10 \cdot \left(\frac{3}{10} \cdot y\right) \]
This simplifies to:
\[ 5x = 3y \]

4. **Rearranging to find the ratio \(x : y\):**
We can rearrange this equation to express the ratio of \(x\) to \(y\):
\[ \frac{x}{y} = \frac{3}{5} \]
Therefore, the ratio \(x : y\) can be written as:
\[ x : y = 3 : 5 \]

5. **Final answer:**
Thus, the final answer is:
\[ x : y = 3 : 5 \]