$\mathrm{A}, \mathrm{B}, \mathrm{C}$ are employed to do a piece of work for $529$. $\mathrm{A}$ and $\mathrm{B}$ together are supposed to do $\frac{19}{23}$ of the work, what should $\mathrm{C}$ be paid?

Eight children and $12$ men complete a certain piece of work in $9$ days. Each child takes twice the time taken by a man to finish the work. In how many days will $12$ men finish the same work?