Ram,Rajan,and Rangan can do a certain work in $6, 12,$ and $24$ days respectively. In what time will they altogether do it? (in days)

$A$ and $B$ can together finish a work in $30$ days. They worked at it for $20$ days and then $B$ left. The remaining work was done by $A$ alone in $20$ more days. $A$ alone can finish the work in (in days):

$P$ and $Q$ working together can complete a certain work in $6 \, \text{days}$. $Q$ alone can do it in $8 \, \text{days}$. In how many $\text{days}$ could $P$ alone finish the same work?

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):

$8$ men can complete a piece of work in $20$ days. $8$ women can complete the same work in $32$ days. In how many days will $5$ men and $8$ women together complete the same work?

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).