$8$ boys and $14$ girls are working together. After working for $3$ days, $5$ boys and $8$ girls leave the work. How many more days will be required to complete the work?
I. $19$ boys and $12$ girls together can complete the work in $18$ days.
II. $16$ boys can complete $\frac{2}{3}$ of the work in $16$ days.
III. In $1$ day, the work done by $3$ boys is equal to the work done by $4$ girls.