${\mathrm{Na}}_2{\mathrm{SO}}_3$ and ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ cannot be distinguished by 

${\mathrm{Na}}_2{\mathrm{SO}}_3$ and ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ cannot be distinguished by addition ${\mathrm{CaCl}}_2$ solution as they both gives same compound.

$\begin{array}{l}{\mathrm{CaCl}}_2+{\mathrm{Na}}_2{\mathrm{SO}}_3\to {\mathrm{CaSO}}_3+2\mathrm{NaCl}\\ {\mathrm{CaCl}}_2+{\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3\to {\mathrm{CaSO}}_3+\mathrm{NaCl}\end{array}$

The correct option is C.