Clock Gain Calculation

Clock gains 8 minutes in 24 hours $= 1440$ minutes. So 1448 minutes of false clock $= 1440$ minutes of true clock. Ratio $= \frac{1440}{1448} = \frac{180}{181}$.

From 8 am to 11 am next day $= 27$ hours $= 1620$ minutes. True time elapsed $= 1620 \times \frac{180}{181} \approx 1611.05$ minutes $= 26$ hours $51$ minutes.

True time $= 8\text{ am} + 26\text{ hrs } 51\text{ min} = 10:51\text{ am}$ next day.