If a job is to be completed in $10 \, \text{days}$,it requires $270 \, \text{persons}$. If $180 \, \text{persons}$ take up the same job,they will finish it in (in $\text{days}$):

If $8$ men or $10$ women can do a piece of work in $50$ days,in what time will $28$ men and $15$ women do it? (in days)

$4$ men and $6$ women complete a work in $8$ days,$2$ men and $9$ women also complete the same work in $8$ days. In how many days will $18$ women complete the work?

$A$ can do a piece of work in $20 \, \text{days}$ and $B$ in $30 \, \text{days}$. They work together for $7 \, \text{days}$ and then, both leave the work. Then, $C$ alone finishes the remaining work in $10 \, \text{days}$. In how many $\text{days}$ will $C$ finish the full work?

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:

If $5$ men and $3$ boys can reap $23 \text{ hectares}$ in $4 \text{ days}$ and if $3$ men and $2$ boys can reap $7 \text{ hectares}$ in $2 \text{ days}$,how many boys must assist $7$ men in order that they may reap $45 \text{ hectares}$ in $6 \text{ days}$?