12 men can do a piece of work in 24 days. How many days are needed to complete the work if 8 men are engaged in the same work?

According to the given data,

${\mathrm{M}}_1 = 12, {\mathrm{D}}_1 = 24$

${\mathrm{M}}_2 = 8, {\mathrm{D}}_2 = ?$

As this is a case of inverse variation, therefore, 

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

$\Rightarrow 12\times 24 = 8\times {\mathrm{D}}_2$

$\Rightarrow {\mathrm{D}}_2 =\frac{12\times 24}{8}$

$\Rightarrow {\mathrm{D}}_2 =\frac{12\times {\displaystyle \stackrel{3}{\cancel{24}}}}{\cancel{8}}$

$\Rightarrow {\mathrm{D}}_2 =36 \mathrm{days}$

Therefore, 8 Men require 36 days for the same work.