$2$ 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?

Raj and Ram working together can do a piece of work in $10 \text{ days}$. Raj alone can do it in $12 \text{ days}$. In how many days will Ram alone do the work?

$P, Q$ and $R$ can do a piece of work in $60$ days,$100$ days and $80$ days respectively. They work together to finish the work and receive $Rs. 2256$. Then $P$ will get (in $Rs.$)

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):

$A$ and $B$ can complete a piece of work in $8$ days,$B$ and $C$ can do it in $12$ days,and $C$ and $A$ can do it in $8$ days. In how many days can $A, B,$ and $C$ together complete the work?

$A$ team of $30$ men is supposed to do a work in $38$ days. After $25$ days,$5$ more men were employed and the work was finished one day earlier. How many days would it have been delayed if $5$ more men were not employed? (in days)