In a Hosur factory, 3/5 of the workers speak Tamil, 1/2 speak Kannada and 1/4 speak both, and 54 workers speak neither. How many workers does the factory have?

At least one $=\frac{3}{5}+\frac{1}{2}-\frac{1}{4}=\frac{17}{20}$, so neither $=\frac{3}{20}$. If $\frac{3}{20}$ is 54 workers, the factory has $54\times \frac{20}{3}=360$. 135 takes away the both-group twice, 216 treats 54 as the quarter who speak both, and 108 treats 54 as the half who do not speak Kannada.