If X is `30%` of Z and Y is `60%` of Z, then X is what percentage of Y?

Answer

To solve the problem step by step, we will first express X and Y in terms of Z, and then find the percentage of X in relation to Y.

### Step-by-Step Solution:

1. **Express X and Y in terms of Z**:
- We know that \( X \) is \( 30\% \) of \( Z \).
\[ X = \frac{30}{100} \times Z = 0.3Z \]
- We also know that \( Y \) is \( 60\% \) of \( Z \).
\[ Y = \frac{60}{100} \times Z = 0.6Z \]

2. **Find the ratio of X to Y**:
- We need to find out what percentage \( X \) is of \( Y \). This can be expressed as:
\[ \text{Percentage of } X \text{ in } Y = \left( \frac{X}{Y} \right) \times 100 \]

3. **Substitute the values of X and Y**:
- Substitute \( X \) and \( Y \) from the previous steps:
\[ \text{Percentage of } X \text{ in } Y = \left( \frac{0.3Z}{0.6Z} \right) \times 100 \]

4. **Simplify the expression**:
- The \( Z \) in the numerator and denominator cancels out:
\[ \text{Percentage of } X \text{ in } Y = \left( \frac{0.3}{0.6} \right) \times 100 \]
- Simplifying \( \frac{0.3}{0.6} \) gives:
\[ \frac{0.3}{0.6} = \frac{3}{6} = \frac{1}{2} \]
- Now, substituting this back:
\[ \text{Percentage of } X \text{ in } Y = \left( \frac{1}{2} \right) \times 100 = 50\% \]

5. **Conclusion**:
- Therefore, \( X \) is \( 50\% \) of \( Y \).