The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity `A=(P^(3)Q^(2))/(sqrtRS)`.
The maximum percentage error in the value of A will be :

Options

A. 0.085
B. 0.06
C. 0.065
D. 0.075

Answer

To find the maximum percentage error in the value of \( A = \frac{P^3 Q^2}{\sqrt{R S}} \), we will use the concept of propagation of errors. The formula for the maximum percentage error in a function of several variables is given by:

\[ \frac{\Delta A}{A} = \left| \frac{\partial A}{\partial P} \frac{\Delta P}{P} \right| + \left| \frac{\partial A}{\partial Q} \frac{\Delta Q}{Q} \right| + \left| \frac{\partial A}{\partial R} \frac{\Delta R}{R} \right| + \left| \frac{\partial A}{\partial S} \frac{\Delta S}{S} \right| \]

In our case, the contributions to the percentage error from each variable are weighted by their respective powers in the equation for \( A \).

### Step-by-step Solution:

1. **Identify the powers of each variable in \( A \)**:
- \( P \) has a power of 3.
- \( Q \) has a power of 2.
- \( R \) has a power of \( -\frac{1}{2} \) (since it is in the denominator under the square root).
- \( S \) has a power of \( -\frac{1}{2} \) (similarly).

2. **Write the formula for the maximum percentage error**:
\[ \text{Percentage Error in } A = 3 \cdot \text{Percentage Error in } P + 2 \cdot \text{Percentage Error in } Q + \frac{1}{2} \cdot \text{Percentage Error in } R + \frac{1}{2} \cdot \text{Percentage Error in } S \]

3. **Substitute the given percentage errors**:
- Percentage error in \( P = 0.5\% \)
- Percentage error in \( Q = 1\% \)
- Percentage error in \( R = 3\% \)
- Percentage error in \( S = 1.5\% \)

Plugging these values into the formula:
\[ \text{Percentage Error in } A = 3 \cdot 0.5\% + 2 \cdot 1\% + \frac{1}{2} \cdot 3\% + \frac{1}{2} \cdot 1.5\% \]

4. **Calculate each term**:
- \( 3 \cdot 0.5\% = 1.5\% \)
- \( 2 \cdot 1\% = 2\% \)
- \( \frac{1}{2} \cdot 3\% = 1.5\% \)
- \( \frac{1}{2} \cdot 1.5\% = 0.75\% \)

5. **Sum all the contributions**:
\[ \text{Total Percentage Error in } A = 1.5\% + 2\% + 1.5\% + 0.75\% = 6.75\% \]

### Conclusion:
The maximum percentage error in the value of \( A \) is \( 6.75\% \).