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. $ ± 13\,\% $
• B. $ ± 15\,\% $
• C. $ ± 9\,\% $
• D. $ ± 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}}$
$\therefore \, \frac{\Delta x}{x} \times 100$
$=\pm\left(3 \frac{\Delta a}{a}+3 \frac{\Delta b}{b}+\frac{\Delta c}{c}+\frac{1}{2} \frac{\Delta d}{d}\right) \times 100 \%$
$=\pm\left(3 \times 2+3 \times 1+2+\frac{1}{2} \times 4\right) \%$
$=\pm(6+3+2+2) \%=\pm 13 \%$