$\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ can do a job in $15$ days. After working with $\mathrm{B}$ and $\mathrm{C}$ for $5$ days. $\mathrm{A}$ leaves and then $\mathrm{B}$ and $\mathrm{C}$ finish it in $20$ days more. In how many days can $\mathrm{A}$ do the job alone?

$10$ men can complete a work in $18$ days. After $6$ days, $5$ more men joined. In how many days will the remaining work be completed? (all the men are equally efficient).

A group of workers decided to finish a work in $10$ days but $5$ of them could not join the team. If the rest of the crew completed the job in $12$ days, then number of members present originally in the team were: