$A$ can do a piece of work in $24$ days,$B$ in $32$ days,and $C$ in $64$ days. All begin to do it together,but $A$ leaves $6$ days before the completion of the work. How many days did the work last?

$A$ can do a certain job in $12$ days. $B$ is $60\%$ more efficient than $A$. How many days would $B$ alone take to do the same job?

$A$ can complete a work in $10$ days,$B$ in $12$ days,and $C$ in $15$ days. All of them began the work together; but $A$ had to leave the work after $2$ days of the start and $B$ also left $3$ days before the completion of the work. How long did the work last? (in days)

$10$ women can complete a work in $7$ days and $10$ children take $14$ days to complete the work. How many days will $5$ women and $10$ children take to complete the work?

$A$ contract is to be completed in $50 \text{ days}$ and $105 \text{ men}$ were set to work,each working $8 \text{ hours a day}$. After $25 \text{ days}$,$\frac{2}{5}$ of the work is finished. How many additional men must be employed so that the work may be completed on time,with each man now working $9 \text{ hours a day}$?

$A$ and $B$ can complete a piece of work in $15$ days and $10$ days respectively. They contracted to complete the work for $Rs. 30000$. The share of $A$ in the contracted money will be (in $Rs.$)