Mom prepared orange juice for Jirka's birthday party by mixing 1 liter of $100\%$ juice with $\frac{2}{3}$ liter of $30\%$ juice. Jirka poured himself a glass and tasted it. Since he prefers a weaker concentration, he topped up the prepared juice to its original amount. The resulting juice had a concentration of $61.2\%$, which suited him. How much juice did Jirka pour into his glass?

(M. Raabová)
Let's form the equation

$$
1 \cdot 100+\frac{2}{3} \cdot 30=\left(1+\frac{2}{3}\right) \cdot x
$$

where $x$ is the concentration of the mixture of two types of juice, and solve it:

$$
100+20=\frac{5}{3} x \quad \Rightarrow \quad x=72 .
$$

The concentration of the mixture is $72\%$. Now, let's denote $y$ as the amount of juice Jirka poured out. We will form and solve another equation:

$$
\left(\frac{5}{3}-y\right) \cdot 72=\frac{5}{3} \cdot 61.2 \quad \Rightarrow \quad y=0.25
$$

Jirka poured out 0.25 of the juice.