$A$ can do a piece of work in $30$ days while $B$ can do it in $40$ days. In how many days can $A$ and $B$ working together do it?

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

$A, B$ and $C$ together can finish a piece of work in $4$ days. $A$ alone can do it in $12$ days and $B$ alone in $18$ days. How many days will be taken by $C$ to do it alone?

Ram and Hari can cut $12 \, kg$ of nuts in $2 \, days$. After $5 \, days$, Hari left the work. Ram took $8$ more days to cut the rest of the nuts. If a total of $58 \, kg$ of nuts were cut, the time taken by Hari to cut $10 \, kg$ of nuts is (in days):

$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together is:

$A$ can do a work in $15 \text{ days}$ and $B$ in $20 \text{ days}$. If they work together on it for $4 \text{ days}$,then the fraction of the work that is left is