A physical quantity x is being calculated by measuring y and z and using the formula x = y .z. .In a particular set of values, the value of y is measured with an error + 10%, whereas the value of z is measured with an error of +10%. For this particular set of values the error in the calculation of x will be

Answer

To solve the problem, we need to determine the error in the calculation of the physical quantity \( x \) given the formula \( x = y \cdot z \) and the errors in the measurements of \( y \) and \( z \).

### Step-by-Step Solution:

1. **Understanding the Formula**:
The physical quantity \( x \) is defined as the product of \( y \) and \( z \):
\[ x = y \cdot z \]

2. **Identifying the Errors**:
The error in the measurement of \( y \) is given as \( +10\% \) and the error in the measurement of \( z \) is also \( +10\% \).

3. **Calculating the Effect of Errors**:
When multiplying two quantities, the relative errors add up. Therefore, the total error in \( x \) can be calculated as:
\[ \text{Error in } x = \text{Error in } y + \text{Error in } z \]
Since both errors are \( +10\% \):
\[ \text{Error in } x = 10\% + 10\% = 20\% \]

4. **Conclusion**:
Thus, the total percentage error in the calculation of \( x \) is:
\[ \text{Total Percentage Error in } x = 20\% \]

### Final Answer:
The error in the calculation of \( x \) will be \( 20\% \).

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