$A$ 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 $Rs.$)

$P, Q$ and $R$ contract a work for $Rs. 550$. Together,$P$ and $Q$ are supposed to do $\frac{7}{11}$ of the work. How much does $R$ get? (in $Rs.$)

$A$ is twice as good a workman as $B$. Working together,they finish a piece of work in $1.5$ days. $A$ alone can finish the work in (in days):

$5$ men or $7$ women can earn $Rs. 5,250$ per day. How much would $7$ men and $13$ women earn per day? (in $Rs.$)

$A$ and $B$ can do a job alone in $12 \text{ days}$ and $15 \text{ days}$ respectively. $A$ starts the work and after $6 \text{ days}$,$B$ also joins to finish the work together. For how many days did $B$ actually work on the job?

Twenty-four men can complete a work in sixteen $days$. Thirty-two women can complete the same work in twenty-four $days$. Sixteen men and sixteen women started working and worked for twelve $days$. How many more men are to be added to complete the remaining work in $2$ $days$?