$A$ man,a woman,and a boy can complete a job in $3, 4,$ and $12$ days respectively. How many boys must assist $1$ man and $1$ woman to complete the job in $\frac{1}{4}$ of a day?

$10$ men working $6\, \text{h}$ a day can complete a work in $18\, \text{days}$. How many $\text{hours per day}$ must $15$ men work to complete the same work in $12\, \text{days}$?

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

$A$ is thrice as good a workman as $B$,therefore,$A$ is able to finish a piece of work in $60 \, days$ less than $B$. The time (in $days$) in which they can do it working together is

$15$ men take $20$ days to complete a job working $8$ hours a day. How many hours a day should $20$ men work to complete the same job in $12$ days?

$A$ contractor has the target of completing a work in $40 \text{ days}$. He employed $20$ persons who completed $\frac{1}{4}$ of the work in $10 \text{ days}$ and left. The number of additional persons he has to employ to finish the remaining part of the work as per the target is: