$A$ and $B$ working separately can do a piece of work in $9$ and $15 \, \text{days}$ respectively. If they work on alternate days beginning with $A$,then the work will be completed in how many days?

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?

$45$ men can complete a work in $16$ days. Four days after they started working,$36$ more men joined them. How many days will they now take to complete the remaining work?

$60$ men could complete a work in $250$ days. They worked together for $200$ days. After that,the work had to be stopped for $10$ days due to bad weather. How many more men should be engaged to complete the work on time?

$A$ can complete a work in $6 \, days$ while $B$ can complete the same work in $12 \, days$. If they work together and complete it,the portion of the work done by $A$ is:

$A$ and $B$ can together finish a work in $30$ days. They worked at it for $20$ days and then $B$ left. The remaining work was done by $A$ alone in $20$ more days. $A$ alone can finish the work in (in days):