A physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows: $P = a^3 b^2 / c\sqrt{d}$. The percentage errors of measurement in $a, b, c$ and $d$ are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity $P$ is:

For the relation $P = \frac{a^3 b^2}{c d^{1/2}}$, maximum fractional error is given by: $\frac{\Delta P}{P} = 3\left(\frac{\Delta a}{a}\right) + 2\left(\frac{\Delta b}{b}\right) + 1\left(\frac{\Delta c}{c}\right) + \frac{1}{2}\left(\frac{\Delta d}{d}\right)$. Expressed in percentage errors: $\% \Delta P = 3(1\%) + 2(3\%) + 1(2\%) + \frac{1}{2}(4\%) = 3\% + 6\% + 2\% + 2\% = 13\%$.