5.33 g of CrCl_3 · 6H_2O , which is a 1 : 3 electrolyte, is...

Molar mass of $CrCl_3 \cdot 6H_2O = 52 + 3 \times 35.5 + 6 \times 18 = 266.5 \text{ g mol}^{-1}$

Moles of complex reacted $= \dfrac{5.33}{266.5} = 0.02 \text{ mol}$

Since the complex is a $1:3$ electrolyte, it dissociates to give one complex cation and three chloride anions. Its formula is $[Cr(H_2O)_6]Cl_3$.

When passed through a cation exchanger, the complex cation is exchanged, and the chloride ions pass into the eluted solution.

Molar mass of $AgCl = 108 + 35.5 = 143.5 \text{ g mol}^{-1}$

Moles of $AgCl$ formed $= \dfrac{8.61}{143.5} = 0.06 \text{ mol}$

The ratio of moles of complex reacted to moles of $AgCl$ formed is:

$\text{Ratio} = \dfrac{0.02}{0.06} = \dfrac{1}{3} = 0.3333...$

This can be written as $33.33 \times 10^{-2}$.

Rounding to the nearest integer, we get $33$.

Answer: $33$