Two men can do a piece of work in $x$ days. But $y$ women can do it in $3$ days. Then the ratio of the work done by $1$ man and $1$ woman is

Some staff promised to do a job in $18 \, days,$ but $6$ of them went on leave. So,the remaining men took $20 \, days$ to complete the job. How many men were there originally?

$4$ men and $6$ women complete a work in $8$ days,$2$ men and $9$ women also complete the same work in $8$ days. In how many days will $18$ women complete the work?

$A$ piece of work can be completed by $10$ men and $6$ women in $18$ days. Men work $9$ hours per day while women work $7.5$ hours per day. The per hour efficiency of a woman is $\frac{2}{3}$ of a man's efficiency. In how many days will $10$ men and $9$ women complete the work?

$A$ and $B$ can separately complete a piece of work in $20$ days and $30$ days respectively. They worked together for some time,then $B$ left the work. If $A$ completed the rest of the work in $10$ days,then for how many days did $B$ work?

$A$ and $B$ can together complete a task in $18$ hours. After $6$ hours, $A$ leaves. $B$ takes $36$ hours to finish the rest of the task. How many hours would $A$ have taken to do the task if he worked alone?