$A$ can finish a work in $18$ days and $B$ can do the same work in half the time taken by $A$. Then,working together,what part of the same work can they finish in a day?

If $A$ and $B$ together can complete a piece of work in $15$ days and $B$ alone in $20$ days,in how many days can $A$ alone complete the work?

$A$ and $B$ can complete a work in $15$ days and $10$ days respectively. They started doing the work together,but after $2$ days $B$ had to leave and $A$ alone completed the remaining work. In how many days was the whole work completed?

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

$A$ 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?

$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?