Question

If $35$ men can do a piece of work in $30$ days, in how many days will $21$ men can do it?

Answer 1

Let the required number of days be $x$. We know that the number of days is inversely proportional to the number of men working. Thus $x=\frac{k}{21}$, where $k$ is the constant of proportionality. We also know that $30=\frac{k}{35}$ from the given data. Hence $k=35\times 30$. We obtain
$x=\frac{35\times 30}{21}=50$.
Hence $21$ men need $50$ days to complete the work.