1. Use osmotic pressure relation

For a non-electrolyte, $\pi = C R T$ where $C$ is molarity.

Since both solutions have the same osmotic pressure at the same temperature, their molar concentrations must be equal.

So, molarity of solution of $A$ is: $C_A = 0.05\,\text{M}$

2. Find moles of $A$ in the given solution

Volume of solution is approximately $1000\,\text{mL} = 1\,\text{L}$.

Thus moles of $A$ in $1\,\text{L}$ solution are: $n_A = 0.05\times 1 = 0.05\,\text{mol}$

3. Calculate molar mass of $A$

Given mass of $A = 12\,\text{g}$.

$M_A = \frac{\text{mass}}{\text{moles}} = \frac{12}{0.05} = 240\,\text{g mol}^{-1}$

4. Check with empirical formula

Empirical formula of $A$ is $\mathrm{CH_2O}$.

Empirical formula mass: $12 + 2 + 16 = 30$

Molecular mass obtained is: $240 = 30 \times 8$

So molecular formula would be: $\left(\mathrm{CH_2O}\right)_8 = \mathrm{C_8H_{16}O_8}$

This is consistent.

5. Final Answer

The molecular mass of $A$ is: $\boxed{240\,\text{g}}$