In an experiment, the percentage of error occurred in the measurement of physical quantities A , B , C and D…

Given: Percentage error in $A$, $B$, $C$ and $D$ is $1\%$, $2\%$, $3\%$ and $4\%$, respectively.

The maximum percentage error in $X$ is given by,

$\frac{∆X}{X}\times 100=2\left(\frac{∆A}{A}\times 100\right)+\frac{1}{2}\left(\frac{∆B}{B}\times 100\right)+\frac{1}{3}\left(\frac{∆C}{C}\times 100\right)+3\left(\frac{∆D}{D}\times 100\right)$

$\frac{∆X}{X}\times 100=2\times 1+\frac{1}{2}\times 2+\frac{1}{3}\times 3+3\times 4$

$\frac{∆X}{X}\times 100=16\mathrm{\%}$. will be the maximum percentage error in $X$.