$A$ 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?

$A$ certain job was assigned to a group of men to do in $20$ days. But,$12$ men did not turn up for the job and the remaining men did the job in $32$ days. The original number of men in the group was:

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).

$P$ can do $\left(\frac{1}{4}\right)$ of the work in $10$ days. $Q$ can do $40\%$ of the work in $40$ days and $R$ can do $\left(\frac{1}{3}\right)$ of the work in $13$ days. Who will complete the work first?

$A$ works thrice as good as $B$ and is,therefore,able to finish a piece of work in $60 \text{ days}$ less than $B$. Find the time in which they can complete it,working together (in $\text{days}$).

$A, B$ and $C$ are employed to do a piece of work for $Rs. 575$. $A$ and $C$ are supposed to finish $\frac{19}{23}$ of the work together. The amount to be paid to $B$ is (in $Rs.$)