If `x = a/b`, then the maximum percentage error in the measurement of 'x' will be

Options

A. `(Delta a)/(a)/(Delta b)/(b) xx 100%`
B. `(Delta a)/(a) xx (Delta b)/(b) xx 100%`
C. `[(Delta a)/(a) + (Delta b)/(b)] xx 100%`
D. `[(Delta a)/(a) - (Delta b)/(b)] xx 100% `

Answer

To solve the problem of finding the maximum percentage error in the measurement of \( x \) where \( x = \frac{a}{b} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: We are given that \( x = \frac{a}{b} \). To find the maximum percentage error in \( x \), we need to consider the errors in the measurements of \( a \) and \( b \).

2. **Define Percentage Error**: The percentage error in a quantity is defined as:
\[ \text{Percentage Error} = \left( \frac{\Delta \text{Quantity}}{\text{Actual Quantity}} \right) \times 100\% \]
where \( \Delta \text{Quantity} \) represents the absolute error in the measurement.

3. **Calculate Percentage Errors for \( a \) and \( b \)**:
- The percentage error in \( a \) is:
\[ \text{Percentage Error in } a = \frac{\Delta a}{a} \times 100\% \]
- The percentage error in \( b \) is:
\[ \text{Percentage Error in } b = \frac{\Delta b}{b} \times 100\% \]

4. **Combine the Percentage Errors**: Since \( x \) is a quotient of \( a \) and \( b \), the maximum percentage error in \( x \) can be found by adding the percentage errors of \( a \) and \( b \):
\[ \text{Percentage Error in } x = \text{Percentage Error in } a + \text{Percentage Error in } b \]
Thus, we have:
\[ \text{Percentage Error in } x = \left( \frac{\Delta a}{a} \times 100\% \right) + \left( \frac{\Delta b}{b} \times 100\% \right) \]

5. **Final Expression**: This can be simplified to:
\[ \text{Percentage Error in } x = \left( \frac{\Delta a}{a} + \frac{\Delta b}{b} \right) \times 100\% \]

6. **Conclusion**: Therefore, the maximum percentage error in the measurement of \( x \) is given by:
\[ \text{Maximum Percentage Error in } x = \left( \frac{\Delta a}{a} + \frac{\Delta b}{b} \right) \times 100\% \]

### Answer:
The correct option is:
\[ \frac{\Delta a}{a} + \frac{\Delta b}{b} \times 100\% \]