75% of a number x is equal to 2/5 of an another number y. What is the ratio between x and y?

Options

A. `1:5`
B. `13:8`
C. `8:15`
D. `1:3`

Answer

To solve the problem, we need to express the relationship between the two numbers \( x \) and \( y \) given in the question.

1. **Convert the percentage to a fraction:**
- 75% can be expressed as a fraction:
\[ 75\% = \frac{75}{100} = \frac{3}{4} \]
Therefore, 75% of \( x \) is:
\[ \frac{3}{4}x \]

2. **Express the relationship given in the question:**
- According to the question, 75% of \( x \) is equal to \( \frac{2}{5} \) of \( y \):
\[ \frac{3}{4}x = \frac{2}{5}y \]

3. **Cross-multiply to eliminate the fractions:**
- To eliminate the fractions, we can cross-multiply:
\[ 3 \cdot 5 \cdot x = 2 \cdot 4 \cdot y \]
Simplifying this gives:
\[ 15x = 8y \]

4. **Rearranging to find the ratio \( \frac{x}{y} \):**
- To find the ratio \( \frac{x}{y} \), we can rearrange the equation:
\[ \frac{x}{y} = \frac{8}{15} \]

5. **Final ratio:**
- Therefore, the ratio of \( x \) to \( y \) is:
\[ x:y = 8:15 \]