A drum full of rice weighs

Weight of rice in the drum = Weight of the drum full of rice - Weight of the empty drum

$=40 \frac{1}{6}-13 \frac{3}{4}$

$=\left(40+\frac{1}{6}\right)-\left(13+\frac{3}{4}\right)$

$=\frac{241}{6}-\frac{55}{4}$

$=\frac{241}{6}+\left(\right.$ Additive inverse of $\left.\frac{55}{4}\right)$

$=\frac{482-165}{12}$

$=\frac{317}{12}$

$=26 \frac{5}{12} \mathrm{~kg}$

Therefore, the weight of rice in the drum is $26 \frac{5}{12} \mathrm{~kg}$.