2. Two bottles of equal volume are filled with a mixture of water and juice. In the first bottle, the ratio of the quantities of water and juice is $2: 1$, and in the second bottle, it is $4: 1$. If we pour the contents of both bottles into a third bottle, what will be the ratio of the quantities of water and juice in it?
First method:

Let $v_{1}$ and $s_{1}$ be the quantities of water and juice in the first barrel, and $v_{2}$ and $s_{2}$ be the quantities of water and juice in the second barrel, with $V$ being the volume of each of the two barrels.

Then we have:

$$
v_{1}: s_{1}=2: 1 \text{ and } v_{2}: s_{2}=4: 1,
$$

which means

$$
\begin{aligned}
& v_{1}=\frac{2}{3} V \text{ and } s_{1}=\frac{1}{3} V \\
& v_{2}=\frac{4}{5} V \text{ and } s_{2}=\frac{1}{5} V
\end{aligned}
$$

The total quantity of water from both barrels is

$$
v_{3}=v_{1}+v_{2}=\frac{22}{15} V
$$

1 POINT

and the total quantity of juice from both barrels is

$$
s_{3}=s_{1}+s_{2}=\frac{8}{15} V
$$

The ratio of the quantities of water and juice in the third barrel is $v_{3}: s_{3}=\frac{22}{15} V: \frac{8}{15} V=11: 4$.

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