$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together 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)

$2$ 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 $Rs.$)

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18 \text{ days}$ to complete a work,how much time shall $B$ take to do it alone? (in $\text{days}$)

$P$ can complete $\frac{1}{4}$ of a work in $10$ days,$Q$ can complete $40\%$ of the same work in $15$ days,$R$ can complete $\frac{1}{3}$ of the work in $13$ days,and $S$ can complete $\frac{1}{6}$ of the work in $7$ days. Who will be able to complete the work first?

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 $\text{days}$):