$A$ and $B$ can separately do a piece of work in $6 \, \text{days}$ and $12 \, \text{days}$ respectively. How long will they together take to do the work? (in $\text{days}$)

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)

$3$ men and $4$ boys can complete a certain work in $8$ days,while $4$ men and $4$ boys can complete the same work in $6$ days. Then $2$ men and $4$ boys will finish it in ........ days.

$40$ men can complete a work in $40$ days. They started the work together. But at the end of each $10^{th}$ day,$5$ men left the job. The work would have been completed in (in days):

$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

$15$ men take $20$ days to complete a job working $8$ hours a day. How many hours a day should $20$ men work to complete the same job in $12$ days?