$A$ alone can complete a work in $16$ days and $B$ alone in $12$ days. Starting with $A$,they work on alternate days. The total work will be completed in (in days):

$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?

$A$ and $B$ can do a piece of work in $10$ days. $B$ and $C$ can do it in $12$ days. $A$ and $C$ can do it in $15$ days. How long will $A$ take to do it alone? (in days)

$A$ and $B$ together can complete a work in $10$ days. They started together,but $A$ left after $2$ days and the remaining work was completed by $B$ in $12$ days. In how many days can $A$ complete the entire work while working alone?

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

$A$ and $B$ together can complete a work in $30$ days. They started together but after $6$ days $A$ left the work and the work is completed by $B$ after $36$ more days. $A$ alone can complete the entire work in how many days?