$A$ and $B$ can do a piece of work in $8$ days,$B$ and $C$ can do the same work in $12$ days,and $A, B,$ and $C$ together complete it in $6$ days. The number of days required to finish the work by $A$ and $C$ together is:

$A$ and $B$ can complete a piece of work in $6$ days,and $A$ alone can complete it in $9$ days. The time taken by $B$ alone to complete the work is (in days):

$P$ is twice as good a workman as $Q,$ and together they finish a work in $16$ days. In how many days can it be done by each separately?

$A$ can complete a piece of work in $12$ days. $B$ is $60\%$ more efficient than $A$. The number of days that $B$ will take to complete the same work is:

Some staff promised to do a job in $18 \, days,$ but $6$ of them went on leave. So,the remaining men took $20 \, days$ to complete the job. How many men were there originally?

$A$ 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?