If $4$ men or $8$ women can do a piece of work in $15$ days,in how many days can $6$ men and $12$ women do the same piece of work?

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

$A$ certain number of men can do a piece of work in $40 \, days$. If there were $45 \, men$ more,the work could have been finished in $25 \, days$. Find the original number of men employed in the work.

$A$ can do a work in $15 \text{ days}$ and $B$ in $20 \text{ days}$. If they work together on it for $4 \text{ days}$,then the fraction of the work that is left is

Some carpenters promised to do a job in $9$ days,but $5$ of them were absent and the remaining men did the job in $12$ days. The original number of carpenters was:

$15$ men take $20$ days to complete a job working $8$ hours a day. The number of hours a day $20$ men should work to complete the same job in $12$ days is: