$2$ 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?

If $A$ and $B$ together can complete a work in $18$ days,$A$ and $C$ together in $12$ days,and $B$ and $C$ together in $9$ days,then $B$ alone can do the work in (in days)

$A$ does $\frac{2}{5}$ of a work in $9$ days. Then $B$ joined him and they together completed the remaining work in $6$ days. $B$ alone can finish the whole work in (in days):

$A$ can do a piece of work in $20 \, \text{days}$ and $B$ in $30 \, \text{days}$. They work together for $7 \, \text{days}$ and then, both leave the work. Then, $C$ alone finishes the remaining work in $10 \, \text{days}$. In how many $\text{days}$ will $C$ finish the full work?

$x$ number of men can finish a piece of work in $30$ days. If there were $6$ men more,the work could be finished in $10$ days less. The actual number of men is

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).