$x$ 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 complete a piece of work in $45$ and $40$ days respectively. Both started to work together,but after some days $A$ left and $B$ alone completed the remaining work in $23$ days. For how many days did $A$ work?

$A$ can complete a piece of work in $10$ days,while $B$ alone can complete it in $15$ days. They work together for $5$ days and the rest of the work is done by $C$ in $2$ days. If they receive $Rs. 450$ for the whole work,how should they divide the money? (in $Rs.$)

$A$ does $\frac{2}{5}$ of a work in $9$ days. Then $B$ joined him and they together completed the remaining work in $6$ days. $B$ alone can finish the whole work in (in days):

Machine $P$ can print one lakh books in $8$ hours,machine $Q$ can print the same number of books in $10$ hours,while machine $R$ can print them in $12$ hours. All the machines are started at $9.00$ a.m. while machine $P$ is closed at $11.00$ a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?