$A$ can complete a work in $10$ days,$B$ in $12$ days,and $C$ in $15$ days. All of them began the work together; but $A$ had to leave the work after $2$ days of the start and $B$ also left $3$ days before the completion of the work. How long did the work last? (in days)

$A$ contract is to be completed in $50 \text{ days}$ and $105 \text{ men}$ were set to work,each working $8 \text{ hours a day}$. After $25 \text{ days}$,$\frac{2}{5}$ of the work is finished. How many additional men must be employed so that the work may be completed on time,with each man now working $9 \text{ hours a day}$?

$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together is:

$10$ men can cut $15$ trees in $2$ hours. If $2$ men leave the job,how many trees will be cut in $3$ hours?

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work get completed?

$4$ men and $6$ women complete a work in $8$ days,$2$ men and $9$ women also complete the same work in $8$ days. In how many days will $18$ women complete the work?