$A$ and $B$ complete a job in $12 \text{ days}$,while $A, B$,and $C$ can complete it in $8 \text{ days}$. $C$ alone will finish the job in (in $\text{days}$):

$P$ can complete a work in $12$ days working $8$ hours a day. $Q$ can complete the same work in $8$ days working $10$ hours a day. If both $P$ and $Q$ work together,working $8$ hours a day,in how many days can they complete the work?

$A$ and $B$ together can complete a work in $8$ days. $B$ alone can complete that work in $12$ days. $B$ alone worked for $4$ days. After that,how long will $A$ alone take to complete the remaining work?

$A$ can do a piece of work in $20 \, \text{days}$ and $B$ in $30 \, \text{days}$. They work together for $7 \, \text{days}$ and then, both leave the work. Then, $C$ alone finishes the remaining work in $10 \, \text{days}$. In how many $\text{days}$ will $C$ finish the full work?

$A$ and $B$ undertake a piece of work for $Rs. 250$. $A$ alone can do that work in $5$ days and $B$ alone can do that work in $15$ days. With the help of $C$,they finish the work in $3$ days. If everyone gets paid in proportion to the work done by them,the amount $C$ will get is (in $Rs.$)

$A$ does half as much work as $B$ in $three-fourths$ of the time. If together they take $18$ days to complete a work,how much time shall $B$ take to do it alone? (in days)