6 men can finish digging a well 16 days. How many days will 8 men take to complete the same amount of work?

It is given that,

Initially, the number of men, ${\mathrm{M}}_1 =6$,  

And, the number of days needed to complete the work, ${\mathrm{D}}_1 = 16$  

Then, the number of men, ${\mathrm{M}}_2=8,$  

and, let the number of days needed to complete the work be D₂.

Since the same amount of work is done in both scenarios, we write,

As, this is a case on inverse variation, therefore,

${\mathrm{M}}_1{\mathrm{D}}_1 = {\mathrm{M}}_2{\mathrm{D}}_2$

$\Rightarrow$$6\times 16 = 8 \times {\mathrm{D}}_2$

$\Rightarrow$${\mathrm{D}}_2=\frac{6\times 16}{8}$

$\Rightarrow$${\mathrm{D}}_2=\frac{6\times 8\times 2}{8}$

$\Rightarrow$${\mathrm{D}}_2=\frac{6\times \cancel{8}\times 2}{\cancel{8}}$

$\Rightarrow$${\mathrm{D}}_2=6\times 2$

$\Rightarrow$${\mathrm{D}}_2=12 \mathrm{Days}$

8 Men will take 12 days to complete the same work.