If 30% of x is same as 40% of y then what is y : x ?

Options

A. 4 : 3
B. 3 : 4
C. 7 : 4
D. 4 : 7

Answer

To solve the problem, we need to find the ratio of \( y \) to \( x \) given that \( 30\% \) of \( x \) is equal to \( 40\% \) of \( y \).

### Step-by-Step Solution:

1. **Write the equation based on the percentages**:
\[ 30\% \text{ of } x = 40\% \text{ of } y \]
This can be expressed mathematically as:
\[ \frac{30}{100} \cdot x = \frac{40}{100} \cdot y \]

2. **Simplify the fractions**:
\[ \frac{3}{10} \cdot x = \frac{4}{10} \cdot y \]

3. **Eliminate the fractions** by multiplying both sides by \( 10 \):
\[ 3x = 4y \]

4. **Rearrange the equation to find the ratio**:
\[ \frac{y}{x} = \frac{3}{4} \]

5. **Express the ratio in the form of \( y : x \)**:
\[ y : x = 3 : 4 \]

### Final Answer:
The ratio \( y : x \) is \( 3 : 4 \).