## 50. When did the ball start?

- At the last ball, - Dora said during breakfast, - the guests thought the clocks had stopped: the hands were in the same position as at the beginning of the evening. It turned out that the hour and minute hands had simply switched places. As you remember, the ball started between ten and eleven o'clock. Can you name the time more precisely?
50. The evening began at 10:59 \( \frac{83}{143} \) min, and when the guests looked at the hands, which had switched places, they showed 11:54 \( \frac{138}{143} \) min.