If $10$ persons can do a job in $20$ days,then $20$ persons with twice the efficiency can do the same job in (in days)

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work be completed?

$A$ and $B$ together can do a piece of work in $10$ days. $A$ alone can do it in $30$ days. The time in which $B$ alone can do it is (in days):

$A$ track of $100\, m$ can be built by $7\, men$ or $10\, women$ in $70\, days.$ How many days will $14\, men$ and $20\, women$ take to build a track of $600\, m$?

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18$ days to complete a work,then how much time shall $B$ take to complete it? (in days)

$A$ farmer can plough a field working $6 \text{ hours per day}$ in $18 \text{ days}$. How many $\text{hours per day}$ must the farmer work to finish the same work in $12 \text{ days}$?