$A$ can complete a work in $m$ days and $B$ can complete it in $n$ days. How many days will it take to complete the work if both $A$ and $B$ work together?

$A$ and $B$ together can do a piece of work in $30$ days. $A$ having worked for $16$ days,$B$ finishes the remaining work alone in $44$ days. In how many days shall $B$ finish the whole work alone?

$A$ and $B$ can do a work in $12$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can do the same work in $20$ days. How much time will $A, B,$ and $C$ take to complete the same work together (in days)?

Ajay and Sunil together can complete a piece of work in $10$ days,Sunil and Sanjay in $15$ days,and Sanjay and Ajay in $20$ days. They worked together for $6$ days,and then Ajay leaves. Sunil and Sanjay worked together for $4$ more days,and Sunil leaves. How long will Sanjay take to complete the remaining work? (in days)

$A$ is thrice as good a workman as $B$,therefore,$A$ is able to finish a piece of work in $60 \, days$ less than $B$. The time (in $days$) in which they can do it working together is

If $10$ men or $18$ boys can do a work in $15$ days,then the number of days required by $15$ men and $33$ boys to do twice the work is