$2$ 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?

Bansal,Gupta,and Singhal together can complete a work in $4 \, \text{days}$. If Bansal and Gupta together can complete the work in $4 \frac{4}{5} \, \text{days}$,and Gupta and Singhal together can do it in $8 \, \text{days}$,then Gupta alone can complete the work in (in $\text{days}$):

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

Four examiners can examine a certain number of answer papers in $10$ days by working for $5$ hours a day. For how many hours in a day would $2$ examiners have to work in order to examine twice the number of answer papers in $20$ days?

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):

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is: