When x and y are in indirect proportion and if y doubles, then x becomes _________.

Answer

To solve the problem, we need to understand the concept of indirect proportion. When two quantities are in indirect proportion, it means that as one quantity increases, the other quantity decreases.

### Step-by-Step Solution:

1. **Understanding Indirect Proportion**:
- Since x and y are in indirect proportion, we can express this relationship as:
\[ x \propto \frac{1}{y} \]
- This means that \( x \times y = k \) for some constant \( k \).

2. **Initial Relationship**:
- Let’s denote the initial values of x and y as \( x_1 \) and \( y_1 \). Thus, we have:
\[ x_1 \times y_1 = k \]

3. **Doubling y**:
- If y doubles, the new value of y becomes:
\[ y_2 = 2y_1 \]

4. **Finding New Value of x**:
- Since x and y are inversely proportional, we can write:
\[ x_2 \times y_2 = k \]
- Substituting \( y_2 \) into the equation gives:
\[ x_2 \times (2y_1) = k \]

5. **Substituting for k**:
- We know from the initial relationship that \( k = x_1 \times y_1 \). Therefore, we can substitute \( k \) in the equation:
\[ x_2 \times (2y_1) = x_1 \times y_1 \]

6. **Solving for x_2**:
- To find \( x_2 \), we can rearrange the equation:
\[ x_2 = \frac{x_1 \times y_1}{2y_1} \]
- The \( y_1 \) terms cancel out:
\[ x_2 = \frac{x_1}{2} \]

7. **Conclusion**:
- Therefore, when y doubles, x becomes half of its original value:
\[ x = \frac{x_1}{2} \]

### Final Answer:
When y doubles, then x becomes **half** of its original value.

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