If $6$ men and $8$ boys can do a piece of work in $10$ days and $26$ men and $48$ boys can do the same work in $2$ days,the time taken by $15$ men and $20$ boys to do the same type of work will be (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?

$A$ man can do a piece of work in $5$ days,but with the help of his son,he can do it in $3$ days. In what time can the son do it alone? (in days)

$P$ can complete a work in $12$ days working $8$ hours a day. $Q$ can complete the same work in $8$ days working $10$ hours a day. If both $P$ and $Q$ work together,working $8$ hours a day,in how many days can they complete the work?

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10 \text{ days}$ and $C$ alone in $50 \text{ days}$,then $B$ alone could do it in (in $\text{days}$):

$A$ and $B$ can complete a piece of work in $6$ days,and $A$ alone can complete it in $9$ days. The time taken by $B$ alone to complete the work is (in days):