If 36 men can do a piece of work in 25 days,

Let x be the number of days in which 15 men can do a piece of work.

Since the number of men hired and the number of days taken to do a piece of work are in inverse variation, we have:

$36 \times 25=x \times 15$

$\Rightarrow x=\frac{36 \times 25}{15}$

$=\frac{900}{15}$

$=60$

Thus, the required number of days is 60 .