$A$ can do a work in $15\, days$ and $B$ in $20\, days.$ If they work on it together for $4\, days,$ then the fraction of the work that is left is

$A$ can do a work in $12$ days. When he had worked for $3$ days,$B$ joined him. If they complete the work in $3$ more days,in how many days can $B$ alone finish the work?

$A$ does $\frac{1}{5}$ of a work in a $week$. $B$ finishes the same in a fortnight. $B$ starts the work and works only for $3$ days. Thereafter,$A$ completes the job. In how many days will $A$ finish the remaining work?

$P, Q, R$ are employed to do a work for $Rs. 5750$. $P$ and $Q$ together finished $\frac{19}{23}$ of the work,and $Q$ and $R$ together finished $\frac{8}{23}$ of the work. The wage of $Q$ (in rupees) is:

$A$ 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):

$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?