A man purchased some eggs at 3 for ₹ 16 and sold them at 5 for ₹ 36.

Let the number of eggs purchased be $x$.

CP of 3 eggs $=₹ 16$

$\therefore \mathrm{CP}$ of $1 \mathrm{egg}=₹ \frac{16}{3}$

$\Rightarrow \mathrm{CP}$ of $x$ eggs $=₹ \frac{16}{3} x$

SP of 5 eggs $=₹ 36$

$\therefore \mathrm{SP}$ of $1 \mathrm{egg}=₹ \frac{36}{5}$

$\Rightarrow$ SP of $x$ eggs $=₹ \frac{36}{5} x$

Gain $=\mathrm{SP}-\mathrm{CP}=₹ 168$

$\therefore \frac{36}{5} x-\frac{16}{3} x=168$

$\Rightarrow \frac{28}{15} x=168$

$\Rightarrow x=\frac{168 \times 15}{28}$

$\Rightarrow x=90$

Hence, the man purchased 90 eggs.