$A$ man,a woman,and a boy can together complete a piece of work in $3$ days. If a man alone can do it in $6$ days and a boy alone in $18$ days,how long will a woman alone take to complete the work? (in days)

$A$ contractor undertakes to dig a canal $12 \, km$ long in $350 \, days$ and employs $45$ men. After $200 \, days$ he finds that only $4.5 \, km$ of the canal has been completed. Find the number of extra men he must employ to finish the work in time (in $men$).

$A$ and $B$ can do a job together in $7$ days. $A$ is $1\frac{3}{4}$ times as efficient as $B$. The same job can be done by $A$ alone in (in days):

$A$ can complete a work in $10$ days,$B$ can complete the same work in $20$ days,and $C$ in $40$ days. $A$ starts working on the first day,$B$ works on the second day,and $C$ works on the third day. Again,$A$ works on the fourth day,$B$ on the fifth day,and so on. If they continue working in the same way,in how many days will the work be completed?

$A, B$ and $C$ can complete a work in $2 \, h$. If $A$ does the job alone in $6 \, h$ and $B$ in $5 \, h$,how long will it take for $C$ to finish the job alone? (in $h$)

$A$ can do a piece of work in $30$ days while $B$ can do it in $40$ days. In how many days can $A$ and $B$ working together do it?