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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:

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