$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. Then $B$ leaves and $A$ alone continues the work. After $12$ days,$C$ joins $A$ and the work is completed in $48$ days more. In how many days can $C$ do it if he works alone?

$A, B$ and $C$ are employed to do a piece of work for $Rs. 575$. $A$ and $C$ are supposed to finish $\frac{19}{23}$ of the work together. The amount to be paid to $B$ is (in $Rs.$)

$4$ men and $6$ women can complete a work in $8$ days,while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

$A$ can do a piece of work in $16$ days and $B$ in $24$ days. They take the help of $C$ and all three together finish the work in $6$ days. If the total remuneration for the work is $Rs. 400$,what is the amount (in $Rs.$) each will receive in proportion to the work done?

$12$ 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?

$39$ persons can repair a road in $12$ days working $5$ hours per day. In how many days will $30$ persons working $6$ hours per day complete the same work?