If $10$ men can do a piece of work in $12$ days,the time taken by $12$ men to do the same piece of work will be (in days).

$A$ and $B$ together can complete a task in $20$ days. $B$ and $C$ together can complete the same task in $30$ days. $A$ and $C$ together can complete the same task in $40$ days. What is the ratio of the number of days taken by $A$ when completing the same task alone to the number of days taken by $C$ when completing the same task alone?

$A$ and $B$ undertook to do a piece of work for $Rs. 4500$. $A$ alone could do it in $8$ days and $B$ alone in $12$ days. With the assistance of $C$,they finished the work in $4$ days. Then,$C$'s share of the money is (in $Rs.$)

$2$ men and $3$ women can complete a work in $10$ days,while $4$ men can complete it in $10$ days. In how many days will $3$ men and $3$ women complete the work?

$A$ and $B$ can do a job in $6$ and $12$ days,respectively. They began the work together,but $A$ leaves after $3$ days. Then,the total number of days needed for the completion of the work is:

$S, T$ and $U$ can complete a work in $40, 48$ and $60$ days respectively. They received $Rs. 10800$ to complete the work. They begin the work together,but $T$ left $2$ days before the completion of the work and $U$ left $5$ days before the completion of the work. $S$ completed the remaining work alone. What is the share of $S$ (in $Rs.$) from the total money?