In an experiment, four quantities a b c d , , and are measured with percentage error 1%, 2%, 3% and 4%, respectively. Quantity P is calculated as follows $\mathrm{P}=\frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\mathrm{cd}}$, percentage error in P is

$$\begin{gathered} \mathrm{Given}, \mathrm{P}=\frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\mathrm{cd}}, \frac{∆\mathrm{a}}{\mathrm{a}} \mathrm{x} 100\%=1\% \\ \frac{∆\mathrm{b}}{\mathrm{b}} \mathrm{x} 100\%=2\%, \frac{∆\mathrm{c}}{\mathrm{c}} \mathrm{x} 100\%=3\% \\ \mathrm{and} \frac{∆\mathrm{d}}{\mathrm{d}} \mathrm{x} 100\%=4\% \\ \therefore \%\mathrm{error} \mathrm{in} \mathrm{P}=\left(\frac{∆\mathrm{P}}{\mathrm{P}} \mathrm{x} 100\right)\% \\ =\left(\frac{3∆\mathrm{a}}{\mathrm{a}}+\frac{3∆\mathrm{b}}{\mathrm{b}}+\frac{∆\mathrm{c}}{\mathrm{c}}+\frac{∆\mathrm{d}}{\mathrm{d}}\right) \mathrm{x} 100\% \\ =\left(3\frac{∆\mathrm{a}}{\mathrm{a}} \mathrm{x} 100\%+2\frac{∆\mathrm{b}}{\mathrm{b}} \mathrm{x} 100\%+\frac{∆\mathrm{c}}{\mathrm{c}}\mathrm{x} 100\%+\frac{∆\mathrm{d}}{\mathrm{d}}\mathrm{x} 100\%\right) \\ = 3 \mathrm{x} 1\%+2 \mathrm{x} 2\%+3\%+4\%=14\% \end{gathered}$$