$A$ does $\frac{2}{5}$ of a work in $9$ days. Then $B$ joined him and they together completed the remaining work in $6$ days. $B$ alone can finish the whole work in (in days):

$A$ does $\frac{1}{5}$ of a work in a $week$. $B$ finishes the same in a fortnight. $B$ starts the work and works only for $3$ days. Thereafter,$A$ completes the job. In how many days will $A$ finish the remaining work?

$A,$ $B,$ and $C$ can do a work separately in $16,$ $32,$ and $48$ days respectively. They started the work together,but $B$ left $8$ days before and $C$ left $6$ days before the completion of the work. In what time is the work finished? (in days)

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):

$20$ women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is

$A$ 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 $days$)