$A$ can do a piece of work in $15 \text{ days}$. With the help of $A$,$B$ can do it in $6 \frac{2}{3} \text{ days}$. $B$ can do it alone in (in $\text{days}$)

$A$ farmer can plough a field working $6 \text{ hours per day}$ in $18 \text{ days}$. How many $\text{hours per day}$ must the farmer work to finish the same work in $12 \text{ days}$?

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

$A$ and $B$ can complete a piece of work in $18$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $36$ days. $A$ alone can complete the work in (in 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?

$A$ and $B$ can do a piece of work in $20$ days and $12$ days respectively. $A$ started the work alone and then after $4$ days $B$ joined him until the completion of the work. How long did the work last? (in days)