[ Arithmetic. Mental calculation, etc.]

When the barrel is empty by $30 \%$, it contains 30 liters more honey than when it is filled to $30 \%$. How many liters of honey are in a full barrel?
The first method. If the barrel is empty by $30 \%$, it means it is filled to $70 \%$, so 30 liters make up $40 \%$ of its volume. Therefore, $10 \%$ of the volume of the barrel is 7.5 liters, and the entire volume is 75 liters.

The second method. Let the volume of the barrel be $x$ liters. According to the problem: $0.7 x = 0.3 x + 30$. Then $0.4 x = 30$, so $x=$ 75.

## Answer

75 liters.