$x$ number of men can finish a piece of work in $30$ days. If there were $6$ men more,the work could be finished in $10$ days less. The actual number of men is

$A$ and $B$ can together finish a work in $30$ days. They worked together for $20$ days and then $B$ left. After another $20$ days,$A$ finished the remaining work. In how many days can $A$ alone finish the job?

$A, B$ and $C$ can do a piece of work in $16, 32$ and $48$ days,respectively. They started working together,but $C$ left after working $4$ days and $B$ left $2$ days before the completion of the work. The total number of days taken for the completion of the work was (in days):

$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

$A$ can complete a work in $10$ days,$B$ can complete the same work in $20$ days,and $C$ in $40$ days. $A$ starts working on the first day,$B$ works on the second day,and $C$ works on the third day. Again,$A$ works on the fourth day,$B$ on the fifth day,and so on. If they continue working in the same way,in how many days will the work be completed?

$A, B$ and $C$ can do a piece of work in $20, 30$ and $60$ days respectively. In how many days can $A$ do the work if he is assisted by $B$ and $C$ on every third day?