$A$ can do a piece of work in $14$ days,which $B$ can do in $21$ days. They begin together,but $3$ days before the completion of the work,$A$ leaves. The total number of days to complete the work is:

$18$ women can complete a work in $12$ days and $12$ men can complete the same work in $9$ days. In how many days will $8$ men and $8$ women complete that work? (in days)

$A$ completes a piece of work in $4 \text{ days}$ and $B$ completes it in $6 \text{ days}$. If they both work on it together,then the number of days required to complete the same work is (in $\text{days}$):

$A$ man,a woman,and a boy can together complete a piece of work in $3$ days. If a man alone can do it in $6$ days and a boy alone in $18$ days,how long will a woman alone take to complete the work? (in days)

If $4$ men or $8$ women can do a piece of work in $15$ days,in how many days can $6$ men and $12$ women do the same piece of work?

$A$ can complete a work in $10$ days,$B$ can complete the same work in $20$ days,and $C$ in $40$ days. $A$ starts working on the first day,$B$ works on the second day,and $C$ works on the third day. Again,$A$ works on the fourth day,$B$ on the fifth day,and so on. If they continue working in the same way,in how many days will the work be completed?