$A$ 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?

$A$ contractor has the target of completing a work in $40 \text{ days}$. He employed $20$ persons who completed $\frac{1}{4}$ of the work in $10 \text{ days}$ and left. The number of additional persons he has to employ to finish the remaining part of the work as per the target is:

$A$ and $B$ together can complete a work in $3$ days. They start together,but after $2$ days,$B$ left the work. If the work is completed after two more days,in how many days would $B$ alone do the work?

$A$ and $B$ can do a piece of work in $30$ and $36$ days respectively. They began the work together,but $A$ leaves after some days and $B$ finished the remaining work in $25$ days. After how many days did $A$ leave?

$A$ can do a work in $20 \, \text{days}$ and $B$ in $40 \, \text{days}$. If they work on it together for $5 \, \text{days}$, then the fraction of the work that is left is:

$A$ and $B$ together can complete a work in $8$ days. $B$ alone can complete that work in $12$ days. $B$ alone worked for $4$ days. After that,how long will $A$ alone take to complete the remaining work?