If `X = a + b` , 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 + b) - (Delta b)/(a +b)) xx 100%`
C. `((Delta a)/(a + b) + (Delta b)/(a + b)) xx 100%`
D. `((Delta a)/(a) xx (Delta b)/(b)) xx 100%`

Explanation

To find the maximum percentage error in the measurement of \( X \) where \( X = a + b \), we can follow these steps:

### Step 1: Understand the concept of error
When we measure quantities \( a \) and \( b \), each measurement has an associated error. Let's denote the absolute errors in the measurements of \( a \) and \( b \) as \( \Delta a \) and \( \Delta b \) respectively.

### Step 2: Determine the absolute error in \( X \)
Since \( X \) is the sum of \( a \) and \( b \), the absolute error in \( X \) can be calculated as:
\[ \Delta X = \Delta a + \Delta b \]
This means that the total error in \( X \) is the sum of the individual errors in \( a \) and \( b \).

### Step 3: Calculate the percentage error in \( X \)
The percentage error in \( X \) is given by the formula:
\[ \text{Percentage Error} = \left( \frac{\Delta X}{X} \right) \times 100 \]
Substituting the expression for \( \Delta X \):
\[ \text{Percentage Error} = \left( \frac{\Delta a + \Delta b}{X} \right) \times 100 \]

### Step 4: Substitute \( X \) with \( a + b \)
Since \( X = a + b \), we can rewrite the percentage error as:
\[ \text{Percentage Error} = \left( \frac{\Delta a + \Delta b}{a + b} \right) \times 100 \]

### Step 5: Interpret the result
The maximum percentage error in the measurement of \( X \) can be expressed as the sum of the individual percentage errors of \( a \) and \( b \):
\[ \text{Maximum Percentage Error in } X = \left( \frac{\Delta a}{a} \times 100 \right) + \left( \frac{\Delta b}{b} \times 100 \right) \]

### Final Result
Thus, the maximum percentage error in the measurement of \( X \) is the sum of the maximum percentage errors in the measurements of \( a \) and \( b \).

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