$A$ certain job was assigned to a group of men to do in $20$ days. But,$12$ men did not turn up for the job and the remaining men did the job in $32$ days. The original number of men in the group was:

$2$ 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 $Rs.$)

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ in $40 \text{ days}$,while $C$ and $A$ in $60 \text{ days}$. $A, B, C$ together can complete the work in (in $\text{days}$):

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work be completed?

$A$ and $B$ can do a piece of work in $12$ days, $B$ and $C$ in $8$ days, and $C$ and $A$ in $6$ days. How long would $B$ take to do the same work alone? (in days)

$A$ takes three times as long as $B$ and $C$ together to do a job. $B$ takes four times as long as $A$ and $C$ together to do the work. If all the three,working together,can complete the job in $24$ days,then the number of days $A$ alone will take to finish the job is: