$A$ 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.

$A$ and $B$,working together,can complete a piece of work in $12$ days. $B$ and $C$ working together can complete the same piece of work in $16$ days. $A$ worked at it for $5$ days and $B$ worked at it for $7$ days. $C$ finished the remaining work in $13$ days. How many days would $C$ alone take to complete it?

$A$ can do a certain job in $12$ days. $B$ is $60\%$ more efficient than $A$. How many days would $B$ alone take to do the same job?

$A$ and $B$ together can complete a piece of work in $12$ days and $B$ and $C$ together in $15$ days. If $A$ is twice as good a workman as $C$,then in how many days will $B$ alone complete the same work?

Five men and $2$ boys,working together,can complete four times as much work per hour as a man and a boy working together. The ratio of the work completed by a man and a boy is:

One man,$3$ women,and $4$ boys can do a work in $96$ hours,$2$ men and $8$ boys can do it in $80$ hours,and $2$ men and $3$ women can do it in $120$ hours. In how many hours can it be done by $5$ men and $12$ boys? (in hours)