$P$ 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?

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 $8\, \text{hours per day}$?

$3$ women and $18$ children together take $2$ days to complete a piece of work. How many days will $9$ children alone take to complete the piece of work,if $6$ women alone can complete the piece of work in $3$ 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 $B$ working separately can do a piece of work in $10 \text{ days}$ and $15 \text{ days}$ respectively. If they work on alternate days beginning with $A$,in how many days will the work be completed?

$A$ and $B$ can complete a piece of work in $12$ and $18 \text{ days}$ respectively. $A$ begins to do the work and they work alternatively one at a time for $1 \text{ day}$ each. The whole work will be completed in (in $\text{days}$):