$4$ men and $6$ women can complete a work in $8$ days,while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

$P$ is twice as good a workman as $Q,$ and together they finish a work in $16$ days. In how many days can it be done by each separately?

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10 \text{ days}$ and $C$ alone in $50 \text{ days}$,then $B$ alone could do it in (in $\text{days}$):

$P$ and $Q$ working together can complete a certain work in $6 \, \text{days}$. $Q$ alone can do it in $8 \, \text{days}$. In how many $\text{days}$ could $P$ alone finish the same work?

$60$ men could complete a work in $250$ days. They worked together for $200$ days. After that,the work had to be stopped for $10$ days due to bad weather. How many more men should be engaged to complete the work on time?

$A$ 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?