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

$A$ can do a piece of work in $12$ days and $B$ in $15$ days. They work together for $5$ days and then $B$ leaves. The number of days taken by $A$ to finish the remaining work is:

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

Two men can do a piece of work in $x$ days. But $y$ women can do it in $3$ days. Then the ratio of the work done by $1$ man and $1$ woman is

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)