$A$ farmer can plough a field working $6$ hours per day in $18$ days. How many hours per day must the farmer work to finish the same work in $12$ days?

$A$ can complete a work in $10$ days,$B$ in $12$ days,and $C$ in $15$ days. All of them began the work together; but $A$ had to leave the work after $2$ days of the start and $B$ also left $3$ days before the completion of the work. How long did the work last? (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?

Three men $A, B, C$ working together can do a job in $6$ hours less time than $A$ alone,in $1$ hour less time than $B$ alone,and in one-half the time needed by $C$ when working alone. Then $A$ and $B$ together can do the job in (in hours):

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)

$2$ men and $3$ women together or $4$ men together can complete a piece of work in $20$ days. $3$ men and $3$ women will complete the same work in (in days):