Question

Given $x=\frac{a{b}^2}{c^3}$, if the percentage errors in a, b and c are $\pm$ 1%, $\pm$ 3% and $\pm$ 2% respectively, the percentage error in $x$ can be:

• A. $\pm$ 13%
• B. $\pm$ 7%
• C. $\pm$ 18%
• D. $\pm$ 19%

Answer 1

The correct option is A $\pm$ 13%

The given quantity is $x=\frac{a{b}^2}{c^3}$
Maximum percentage error in $x$ is $\frac{\Delta x}{x}\times 100=[\frac{\Delta a}{a}+2\frac{\Delta b}{b}+3\frac{\Delta c}{c}]\times 100$
$\frac{\Delta x}{x}\times 100=[1+2\times 3+3\times 2]=\pm 13$ %