$6$ men or $12$ women can do a piece of work in $20$ days. In how many days can $8$ men and $16$ women do twice as big as this work?

$28$ men can complete a piece of work in $15 \, \text{days}$ and $15$ women can complete the same piece of work in $24 \, \text{days}$. What is the respective ratio between the amount of work done by $30$ men in $1 \, \text{day}$ and the amount of work done by $18$ women in $1 \, \text{day}$?

$A$ takes twice as much time as $B$ and $C$ takes thrice as much time as $B$ to finish a piece of work. Working together they can finish the work in $12$ days. The number of days needed for $A$ to do the work alone is:

$A$ and $B$ can do a piece of work in $12$ days and $15$ days,respectively. They began to work together,but $A$ left after $4$ days. In how many more days would $B$ alone complete the remaining work?

$A$ 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)

$A$ worker can complete a piece of work in $50$ days. On the first day,he works alone. On the second day,one more person joins him,on the third day,one more person joins them,and this process continues until the work is completed. How many days are needed to complete the work?