If $10$ persons can do a job in $20$ days,then $20$ persons with twice the efficiency can do the same job in (in days)

$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. Then $B$ leaves and $A$ alone continues the work. After $12$ days,$C$ joins $A$ and the work is completed in $48$ days more. In how many days can $C$ do it if he works alone?

$18$ boys can do a piece of work in $24$ days. In how many days can $27$ boys do the same 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?

If $10$ men can do a piece of work in $12$ days,the time taken by $12$ men to do the same piece of work will be (in days).

$A$ can complete a work in $10$ days,$B$ in $12$ days,and $C$ in $15$ days. All of them began the work together; but $A$ had to leave the work after $2$ days of the start and $B$ also left $3$ days before the completion of the work. How long did the work last? (in days)