$A$ is $50\%$ as efficient as $B$. $C$ does half of the work done by $A$ and $B$ together in the same time. If $C$ alone does the work in $20 \text{ days}$,then $A, B$,and $C$ together can do the work in (in $\text{days}$):

$A$ alone can do a piece of work in $6$ days and $B$ alone in $8$ days. $A$ and $B$ undertook to do it for $Rs. 3200$. With the help of $C$,they completed the work in $3$ days. How much is to be paid to $C$ (in $Rs.$)?

$A$ contractor undertakes to dig a canal $12 \, km$ long in $350 \, days$ and employs $45$ men. After $200 \, days$ he finds that only $4.5 \, km$ of the canal has been completed. Find the number of extra men he must employ to finish the work in time (in $men$).

$39$ 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?

The work done by a woman in $8\, \text{hours}$ is equal to the work done by a man in $6\, \text{hours}$ and by a boy in $12\, \text{hours}$. If working $6\, \text{hours per day}$,$9$ men can complete a work in $6\, \text{days}$,then in how many $\text{days}$ can $12$ men,$12$ women,and $12$ boys together finish the same work working $8\, \text{hours per day}$?

$A, B$ and $C$ do a job in $6$ days,$12$ days and $15$ days respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. What is the time taken to finish the remaining work? (in days)