$A$ 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)

$A$ piece of work was to be completed in $40$ days. $A$ number of men employed upon it did only half the work in $24$ days. $16$ more men were then set on,and the work was completed in the specified time. How many men were employed at first?

If $16$ men or $20$ women can do a piece of work in $25$ days,in what time will $28$ men and $15$ women do it? (in days)

$A, B$ and $C$ can do a piece of work individually in $8, 10$ 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?

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?

$A$ and $B$ can separately complete a piece of work in $20$ days and $30$ days respectively. They worked together for some time,then $B$ left the work. If $A$ completed the rest of the work in $10$ days,then for how many days did $B$ work?