$A$ is twice as good a workman as $B$ and together they finish a piece of work in $14$ days. The number of days taken by $A$ alone to finish the work is (in 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?

The first man alone can complete a work in $7$ days. The second man alone can do this work in $8$ days. If they work together to complete this work in $3$ days with the help of a boy,and the total payment is $Rs. 1400$,how should the money be divided among them?

$10$ men can complete a piece of work in $15$ days and $15$ women can complete the same work in $12$ days. If all the $10$ men and $15$ women work together,in how many days will the work be completed?

$10$ women can complete a work in $7$ days and $10$ children take $14$ days to complete the work. How many days will $5$ women and $10$ children take to complete the work?

$A$ and $B$ together can complete a piece of work in $12$ days and $B$ and $C$ together in $15$ days. If $A$ is twice as good a workman as $C$,then in how many days will $B$ alone complete the same work?