D. $15$ days
$1$ skilled person can do $\frac{1}{20 \times 5} = 1/100$ of work in $1$ day, so $2$ skilled person do $2/100$ of work in a day.
Similarly, $6$ semi-skilled and $5$ unskilled person can do $6/200$ and $5/300$ of work respectively in $1$ day.
So, together they do $\frac{2}{100}+\frac{6}{200}+{5}{300} = \frac{1}{15}$ of work together in $1$ day, which gives required number of day to complete the work $= 15.$