$10$ men can finish a piece of work in $10$ days,whereas it takes $12$ women to finish it in $10$ days. If $15$ men and $6$ women undertake to complete the work,how many days will they take to complete it?

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

$A, B$,and $C$ are employed to do a piece of work for $Rs. 529$. $A$ and $B$ together are supposed to do $\frac{19}{23}$ of the work,and $B$ and $C$ together are supposed to do $\frac{8}{23}$ of the work. What amount should $A$ be paid? (in $Rs.$)

The work done by a woman in $8\, \text{hours}$ is equal to the work done by a man in $6\, \text{hours}$ and by a boy in $12\, \text{hours}$. If working $6\, \text{hours per day}$,$9$ men can complete a work in $6\, \text{days}$,then in how many $\text{days}$ can $12$ men,$12$ women,and $12$ boys together finish the same work working $8\, \text{hours per day}$?

$A$ and $B$ can do a piece of work in $10$ days. $B$ and $C$ can do it in $12$ days. $A$ and $C$ can do it in $15$ days. How long will $A$ take to do it alone? (in days)