Physics - Error Question with Solution | TestHub

$\begin{array}{rl}& \text{ : Given : }X=\frac{2k^3{l}^2}{m\sqrt{n}}\\ & \frac{\Delta X}{X}=3\frac{\Delta k}{k}+2\frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta n}{n}\end{array}$ Percentage error in $X$ $\begin{array}{rl}\frac{\Delta X}{X}& \times 100=\left(3\frac{\Delta k}{k}+2\frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta n}{n}\right)\times 100\\ & =3\times 1\%+2\times 2\%+3\%+\frac{1}{2}\times 4\%\\ & =3\%+4\%+3\%+2\%=12\%\end{array}$ Hence, the value of $X$ is uncertain by $12\%$.