At $300 \, \text{K}$, a gaseous reaction: $A \rightarrow B + C$ was found to follow first-order kinetics. Starting with pure A, the total pressure at the end of 20 minutes was $100 \, \text{mm Hg}$. The total pressure after the completion of the reaction is $180 \, \text{mm Hg}$. The partial pressure of A (in mm Hg) is