$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

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)

$A$ and $B$ can complete a piece of work in $18$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $36$ days. $A$ alone can complete the work in (in days):

$A$ can finish a work in $24$ days,$B$ in $9$ days,and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (in days):

$4$ men and $6$ women together can complete a work in $8$ days,while $3$ men and $7$ women together can complete it in $10$ days. $20$ women working together will complete it in (in days):

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)