While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

Sita takes twice as much time as Gita to complete a work and Rita does it in the same time as Sita and Gita together. If all three working together can finish the work in $6$ days,then the time taken by each of them to finish the work is (in days):

If $5$ men and $3$ boys can reap $23 \text{ hectares}$ in $4 \text{ days}$ and if $3$ men and $2$ boys can reap $7 \text{ hectares}$ in $2 \text{ days}$,how many boys must assist $7$ men in order that they may reap $45 \text{ hectares}$ in $6 \text{ days}$?

$18$ women can complete a work in $12$ days and $12$ men can complete the same work in $9$ days. In how many days will $8$ men and $8$ women complete that work? (in days)

Twenty-four men can complete a work in sixteen $days$. Thirty-two women can complete the same work in twenty-four $days$. Sixteen men and sixteen women started working and worked for twelve $days$. How many more men are to be added to complete the remaining work in $2$ $days$?