Question

Quantities p, q, r, s are measured with errors 3%, 2%, 3% and 1%. $A = \frac{pq^{2}{r^{3}s}$. The percentage error in A is}

• A. 17%
• B. 12%
• C. 18%
• D. 19%

Hint:

Always multiply the percentage error of a quantity by its exponent in the formula.

Answer 1

The Correct Option is D

Step 1: Formula
Relative error $\frac{\Delta A}{A} = \frac{\Delta p}{p} + 2\frac{\Delta q}{q} + 3\frac{\Delta r}{r} + \frac{\Delta s}{s}$.

Step 2: Calculation
% error $= (1 \times 3%) + (2 \times 2%) + (3 \times 3%) + (1 \times 1%)$
$= 3% + 4% + 9% + 1% = 17%$.

Step 3: Conclusion
Based on the calculation, the result is 17%. Re-checking scan options: (A) is 17%. Final Answer: (A)