One man,$3$ women,and $4$ boys can do a work in $96$ hours,$2$ men and $8$ boys can do it in $80$ hours,and $2$ men and $3$ women can do it in $120$ hours. In how many hours can it be done by $5$ men and $12$ boys? (in hours)

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

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?

$A$ can do a job in $6 \, days$ and $A$ and $B$ can do it together in $2 \, days.$ How many $days$ will be taken by $B$ to do the job alone?

$A$ does $\frac{1}{5}$ of a work in a $week$. $B$ finishes the same in a fortnight. $B$ starts the work and works only for $3$ days. Thereafter,$A$ completes the job. In how many days will $A$ finish the remaining work?

$P$ 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?