If Karan completes an entire work in $27$ days, what fraction of the work can he complete in $3$ days?

Time taken to complete the full work = $27$ days.
Work done in $1$ day = $\frac{1}{27}$
Work done in $3$ days = $3\times \frac{1}{27}=\frac{3}{27}=\frac{1}{9}$
Therefore, Karan can complete $\frac{1}{9}$ of the work in $3$ days.