$A$ job can be completed by $12$ men in $12$ days. How many extra days will be needed to complete the job if $6$ men leave after working for $6$ days?

If $5$ men and $3$ boys can reap $23 \text{ hectares}$ in $4 \text{ days}$ and if $3$ men and $2$ boys can reap $7 \text{ hectares}$ in $2 \text{ days}$,how many boys must assist $7$ men in order that they may reap $45 \text{ hectares}$ in $6 \text{ days}$?

$A$ and $B$ can do a work in $12$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can do the same work in $20$ days. How much time will $A, B,$ and $C$ take to complete the same work together (in days)?

$A$ and $B,$ working separately,can complete a piece of work in $9$ and $12$ days,respectively. If they work for a day alternately,$A$ beginning,in how many days will the work be completed?

$A$ can do a piece of work in $30$ days while $B$ can do it in $40$ days. In how many days can $A$ and $B$ working together do it?

$A$ and $B$ can do a piece of work in $18$ days,$B$ and $C$ in $24$ days,and $A$ and $C$ in $36$ days. In what time can they do it all working together? (in days)