$A$ 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 $600\, m$?

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

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)

$39$ persons can repair a road in $12$ days working $5$ hours per day. In how many days will $30$ persons working $6$ hours per day complete the same work?

$A$ and $B$ together can complete a work in $10$ days. They started together,but $A$ left after $2$ days and the remaining work was completed by $B$ in $12$ days. In how many days can $A$ complete the entire work while working alone?

$A, B$ and $C$ can do a piece of work in $30, 20$ and $10$ days respectively. $A$ is assisted by $B$ on one day and by $C$ on the next day,alternately. How long would the work take to finish? (in days)