If $8$ men or $10$ women can do a piece of work in $50$ days,in what time will $28$ men and $15$ women do it? (in days)

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together,but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was:

$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. Then $B$ leaves and $A$ alone continues the work. After $12$ days,$C$ joins $A$ and the work is completed in $48$ days more. In how many days can $C$ do it if he works alone?

$A$ 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 $\text{days}$):

$P, Q$ and $R$ can finish a work in $10, 12$ and $15$ days respectively. If $Q$ stops after $2$ days,how long would it take $P$ and $R$ to finish the remaining work? (in days)

$A$ 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: