A and B can finish a work in 20 days.

It is given that $\mathrm{A}$ and $\mathrm{B}$ can finish the work in 20 days.

$\therefore$ Work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\frac{1}{20}$

Now, A alone can do $\frac{1}{5}$ th of the work in 12 days.

$\therefore$ Time taken by A alone to complete the work $=(5 \times 12)=60$ days

$\Rightarrow$ Work done by A in 1 day $=\frac{1}{60}$

Now, work done by $B$ in 1 day $=$ Work done by $(A+B)$ in 1 day work $-$ Work done by $A$ in 1 day

$=\frac{1}{20}-\frac{1}{60}$

$=\frac{3-1}{60}=\frac{2}{60}$

Thus, $\mathrm{B}$ alone can polish the floor in $\frac{60}{2}$ days or 30 days.