Question

The relation gives the value of $x$ as $x$ $=\frac{\left(a^3{b}^3\right)}{\left(c\sqrt{d}\right)}$ . Find the percentage error in $x$, if the percentage error in $a$ , $b$ , $c$ , $d$ , are $2\%$ , $1\%$ , $2\%$ , and $4\%$ respectively :

• A. $\pm 13\%$
• B. $\pm 15\%$
• C. $\pm 9\%$
• D. $\pm 8\%$

Answer 1

Answer: (A)

Maximum probable percentage error
$=\frac{\text{ maximum probable error }}{\text{ observed value }}\times 100$
Given, $x=\frac{a^3{b}^3}{c\sqrt{d}}$
$\therefore \frac{\Delta x}{x}\times 100$
$=\pm \left(3\frac{\Delta a}{a}+3\frac{\Delta b}{b}+\frac{\Delta c}{c}+\frac{1}{2}\frac{\Delta d}{d}\right)\times 100\%$
$=\pm \left(3\times 2+3\times 1+2+\frac{1}{2}\times 4\right)\%$
$=\pm (6+3+2+2)\%=\pm 13\%$