2. At 8 PM, two equally long candles were lit. After some time, the candles were extinguished, and it was observed that the remaining part of the first candle was 4 times larger than the remaining part of the second candle. Calculate at what time the candles were extinguished, given that the first candle burns out in 5 hours, and the second in 4 hours.
Solution. Let $a$ be the length of the candles. Then, in $x$ hours, the first candle will burn $\frac{a}{5} x$, and the second $\frac{a}{4} x$. Thus, the remaining part of the first candle is $a-\frac{a}{5} x$, and of the second $a-\frac{a}{4} x$. According to the condition of the problem, the remainder of the first candle is 4 times larger than the remainder of the second candle, so we have:

$$
a-\frac{a}{5} x=4\left(a-\frac{a}{4} x\right)
$$

Upon solving the equation, it is observed that the length of the candle does not affect the solution. We get $x=3 \text{ h } 45 \text{ min}$, which means the candles were extinguished at 23 hours and 45 minutes.