$A$ 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?

$A, B$ and $C$ can complete a work in $2 \, h$. If $A$ does the job alone in $6 \, h$ and $B$ in $5 \, h$,how long will it take for $C$ to finish the job alone? (in $h$)

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?

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).

$P, Q$ and $R$ contract a work for $Rs. 550$. Together,$P$ and $Q$ are supposed to do $\frac{7}{11}$ of the work. How much does $R$ get? (in $Rs.$)

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?