To find the time difference between 12:30am and 1:20pm, we can break it into two parts: from 12:30am to 12:00pm (noon) and from 12:00pm to 1:20pm. In LaTeX:

From 12:30am to 12:00pm:

\[\text{11 hrs } 30 \text{ min}\]

From 12:00pm to 1:20pm:

\[1 \text{ hr } 20 \text{ min}\]

Now, we add the two intervals together:

\[\begin{aligned}

&\text{11 hrs } 30 \text{ min} \\

+ \ &1 \text{ hr } 20 \text{ min} \\

\hline

&x \text{ hrs } y \text{ min}

\end{aligned}\]

Summing the time intervals, we get:

\[x \text{ hrs } y \text{ min} = \text{12 hrs } 50 \text{ min}\]