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Solution

Clock reading from $8$ a.m. to next day $1$ p.m.: $ 29\ \text{hours (clock time)} $ Clock gains $10$ minutes in $24$ hours ⇒ it runs $\dfrac{145}{144}$ times faster. Real time: $ 29 \times \dfrac{144}{145} = 28.8\ \text{hours} $ $ 0.8\text{ hrs} = 48\text{ min} $ Add $28$ hours $48$ minutes to $8$ a.m.: $ 8\text{ a.m.} + 28\text{ hrs} = 12\text{ noon next day} $ Then $+48$ minutes = $12:48$ p.m.