Sixteen men can complete a work in $15$ days,$24$ children can do the same work in $20$ days. In how many days will $8$ men and $8$ children complete the same work?

$A$ can finish a work in $24$ days,$B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (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?

$2$ 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?

$A$ man and a boy received $Rs. 800$ as wages for $5$ days for the work they did together. The man's efficiency in the work was three times that of the boy. What are the daily wages of the boy? (in $Rs.$)

$12$ men can complete a piece of work in $4$ days,while $15$ women can complete the same work in $4$ days. $6$ men start working on the job and after working for $2$ days,all of them stopped working. How many women should be put on the job to complete the remaining work,if it is to be completed in $3$ days?