Problem of time

First we convert to time to 24-hour system $\text{06:27 PM} = \text{18:27 H}$ . Then consider

$\begin{aligned} \underbrace{00}_h:\underbrace{2880717}_{min} & = \underbrace{48011}_h: \underbrace{57}_{min} = \underbrace{2000}_{days}:\underbrace{11}_h: \underbrace{57}_{min} = \underbrace{\text{11:57 H}}_{\text{Time of the day}} \end{aligned}$

Therefore, the time of the day 2880717 minutes ago $\text{18:27 H} - \text{11:57 H} = \text{06:30 H} = \boxed{\text{06:30 AM}}$ .

Every day has $60 \cdot 24 = 1440$ minutes.

Since $2880717 \equiv 717 \bmod 1440$ , there will be 717 minutes more than a whole number of days.

$717 = 11 \cdot 60 + 57$ , so aftsr these days, there are 11 hours and 57 minutes more, so 3 minutes less than 12 hours.

12 hours before 6:27 pm is 6:27 am, and 3 minutes later than that is 6:30 am .