$A$ can do a work in $10 \text{ days}$ and $B$ in $20 \text{ days}$. If they work together on it for $5 \text{ days}$,then the fraction of the work that is left is:

While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (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 $\text{days}$):

$A$ can do a piece of work in $12$ days and $B$ in $20$ days. If they together work on it for $5$ days and the remaining work is completed by $C$ in $3$ days, then in how many days can $C$ do the same work alone?

$8$ children and $12$ men complete a certain piece of work in $9$ days. If 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?

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)