Question

The percentage errors in a, b, c are $\pm 1$%, $\pm 3$% and $\pm 2$% respectively. The percentage error in $\frac{a^2}{b{c}^3}$ is:

• A. $\pm 13$%
• B. $\pm 9$%
• C. $\pm 6$%
• D. $\pm 11$%

Answer 1

Answer: (D)

$\pm 11$%

Let $Y=\frac{a^2}{b{c}^3}$
$\frac{\Delta Y}{Y}\times 100=\pm (2\times \frac{\Delta a}{a}\times 100+\frac{\Delta b}{b}\times 100+3\times \frac{\Delta c}{c}\times 100)$
$=\pm (2\times 1+3+3\times 2)$

$=\pm 11$