$3$ men and $4$ women can finish a work in $12$ days whereas $5$ men and $4$ women can complete the same work in $9$ days. Find the ratio of the amount of work done by a man to the amount of work done by a woman.

If $5$ workers can earn $₹17500$ in $10$ days, then how many workers will earn $₹29400$ rupees in $7$ days?

A group of labourers is hired to complete the work in $12$ days, but three of them do not come work. Find the original number of labourers in the group, if the remaining labourers completed the work in $15$ days.

$A$ can do a piece of work in $10$ days and $B$ in $15$ days. If both of them work together, then they will take $k$ days to finish the work​. The value of $k$ is

$A$ and $B$ can finish a piece of work in $20$ days and $30$ days respectively, if they work separately. If both of them work together, then they will take $k$ days to finish the work​. The value of $k$ is

$A$ and $B$ together can paint an apartment in $4$ days. $A$ alone takes $6\mathit{}$ days to paint the apartment. If $B$ alone can paint the apartment in $k$ days, then find the value of $k$.

$A$ and $B$ together can complete a piece of work in $12$ days while $B$ alone can finish it in $30$ days. If $A$ alone can finish the work in $k$ days, find the value of $k$.

$A$ and $B$ can complete a piece of work in $20$ days, $B$ and $C$ in $15$ days and $C$ and $A$ in $12$ days. In how many days will they complete the work together? In how many days will they complete the work separately?

$A$ can do a piece of work in $15$ days and $B$ in $\mathit{}20$ days. With the help of $C$, the work gets finished in $5$ days. If $C$ will take $k$ days to finish the work alone, then the value of $k$.