$A$ is twice as good a workman as $B$. Working together,they finish a piece of work in $1.5$ days. $A$ alone can finish the work in (in days):

$A$ and $B$ can do a work in $12$ days,$B$ and $C$ in $15$ days,and $C$ and $A$ in $20$ days. If $A, B,$ and $C$ work together,they will complete the work in (in days):

$A$ and $B$ together can complete a work in $3$ days. They start together,but after $2$ days,$B$ left the work. If the work is completed after two more days,in how many days would $B$ alone do the work?

$A$ and $B$ can complete a work in $15$ days and $10$ days respectively. They started doing the work together,but after $2$ days $B$ had to leave and $A$ alone completed the remaining work. In how many days was the whole work completed?

$A$ 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)

$A$ can do $\frac{1}{3}$ of a work in $5 \text{ days}$ and $B$ can do $\frac{2}{5}$ of the work in $10 \text{ days}$. In how many $\text{days}$ can both $A$ and $B$ together do the work?