$2$ men and $5$ women can finish a piece of work in $12$ days. $5$ men and $2$ women can finish the same work in $9$ days. In how many days can $3$ women finish the same work?

$2$ men and $1$ woman can do a piece of work in $14$ days,while $4$ women and $2$ men can do the same work in $8$ days. If a man gets $Rs. 90$ per day,what should be the wages per day of a woman? (in $Rs.$)

There is sufficient food for $400$ men for $31$ days. After $28$ days,$280$ men leave the place. For how many days will the rest of the food last for the rest of the men? (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 $men$).

$P$ is twice as good a workman as $Q,$ and together they finish a work in $16$ days. In how many days can it be done by each separately?

$A, B$ and $C$ can complete a piece of work in $15, 30$ and $40$ days respectively. They started the work together,but $A$ left $2$ days before the completion of the work and $B$ left $4$ days before the completion of the work. In how many days was the work completed?