$A$ 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):

$A$ worker can complete a piece of work in $50$ days. On the first day,he works alone. On the second day,one more person joins him,on the third day,one more person joins them,and this process continues until the work is completed. How many days are needed to complete the work?

Some staff promised to do a job in $18 \, days,$ but $6$ of them went on leave. So,the remaining men took $20 \, days$ to complete the job. How many men were there originally?

$A$ alone can complete a work in $18 \, days$ and $B$ alone in $15 \, days.$ $B$ alone worked at it for $10 \, days$ and then left the work. In how many more days will $A$ alone complete the remaining work?

If a job is to be completed in $10 \, \text{days}$,it requires $270 \, \text{persons}$. If $180 \, \text{persons}$ take up the same job,they will finish it in (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 $Rs.$)