In an experiment four quantities $p, q, r$ and $s$ are measured with percentage $3 \%, 2 \%, 3 \%$ and $1 \%$ respectively. Quantity ' A ' is calculated as follows $\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}$, the percentage error in ' A ' is

Given $A = \frac{pq^2}{r^2 s^4}$, the maximum percentage error is calculated using the formula for error propagation in products and quotients.

For $A = p^1 q^2 r^{-2} s^{-4}$, the percentage error is:

$\left(\frac{\Delta A}{A} \times 100\right)\% = |1|\left(\frac{\Delta p}{p} \times 100\right)\% + |2|\left(\frac{\Delta q}{q} \times 100\right)\% + |-2|\left(\frac{\Delta r}{r} \times 100\right)\% + |-4|\left(\frac{\Delta s}{s} \times 100\right)\%$

Substituting the given percentage errors $3\%$ for $p$, $2\%$ for $q$, $3\%$ for $r$, and $1\%$ for $s$:

$\left(\frac{\Delta A}{A} \times 100\right)\% = 1 \times 3\% + 2 \times 2\% + 2 \times 3\% + 4 \times 1\% = 3\% + 4\% + 6\% + 4\% = 17\%$

Final answer: $\boxed{A}$