Step 1: Identify the property that is equal.
Both solutions have the same osmotic pressure at the same temperature $27^{\circ}C$. Osmotic pressure is a colligative property given by $\Pi = CRT$, so if $\Pi$ and $T$ are equal, the molar concentrations $C$ must be equal too.
Step 2: Note that both volumes are 1.0 L.
Since both solutions are made in $1.0$ L, molarity is simply moles divided by $1$, which equals the number of moles. So equal concentration means equal moles of solute.
Step 3: Write moles in terms of given masses.
Moles of glucose $= \dfrac{x}{180}$ and moles of the other solute $= \dfrac{y}{92}$.
Step 4: Set the moles equal.
Because the concentrations match, \[ \frac{x}{180} = \frac{y}{92} \]
Step 5: Rearrange to get the ratio x/y.
Cross multiplying gives \[ \frac{x}{y} = \frac{180}{92} \]
Step 6: Simplify the fraction.
Dividing top and bottom by $4$, we get $\dfrac{180}{92} = \dfrac{45}{23}$. So the required ratio is $45/23$.
\[ \boxed{\dfrac{45}{23}} \]