$A, B$ and $C$ can do a piece of work individually in $8, 12$ and $15$ days,respectively. $A$ and $B$ start working,but $A$ quits after working for $2$ days. After this,$C$ joins $B$ until the completion of the work. In how many days will the work be completed?

$A$ can do a piece of work in $30$ days,$B$ in $50$ days,and $C$ in $40$ days. If $A$ is assisted by $B$ on one day and by $C$ on the next day alternately,the work will be completed in (in days):

$A$ and $B$ working separately can do a piece of work in $10 \text{ days}$ and $15 \text{ days}$ respectively. If they work on alternate days beginning with $A$,in how many days will the work be completed?

$A$ and $B$ together can complete a work in $10$ days. They started together,but $A$ left after $2$ days and the remaining work was completed by $B$ in $12$ days. In how many days can $A$ complete the entire work while working alone?

$A$ does a work in $10$ $days$ and $B$ does the same work in $15$ $days$. In how many $days$ will they together do the same work?

$6$ men can complete a piece of work in $12$ days. $8$ women can complete the same piece of work in $18$ days,whereas $15$ children can complete the piece of work in $10$ days. $4$ men,$12$ women,and $20$ children work together for $2$ days. If only men were to complete the remaining work in $1$ day,how many men would be required?