1. In a cup, there is 3 dl of white coffee. The ratio of milk to coffee in this mixture is $3: 2$. Marko drank a sixth of the white coffee and then topped up the cup to the brim with milk. After that, he drank a fifth of the white coffee and refilled the cup to the brim, adding five times more milk than coffee. After drinking a part of the white coffee for the third time, the cup was one-third full of white coffee. How much milk will be in the cup after Marko refills it to the brim with milk again?
## First Solution.

The ratio of the quantities of milk and coffee in the mixture is $3:2$, so we conclude that there are a total of $3+2=5$ equal parts. Thus, $\frac{3}{5}$ of the mixture is milk and $\frac{2}{5}$ is coffee.

$\frac{3}{5}$ of $3 \mathrm{dl}$ is $1.8 \mathrm{dl}, 3 \mathrm{dl}-1.8 \mathrm{dl}=1.2 \mathrm{dl}$.

At the beginning, there is $1.8 \mathrm{dl}$ of milk and $1.2 \mathrm{dl}$ of coffee in the cup.

$\frac{1}{6}$ of $1.8 \mathrm{dl}$ is $0.3 \mathrm{dl}, \frac{1}{6}$ of $1.2 \mathrm{dl}$ is $0.2 \mathrm{dl}$.

After the first sip, the cup contains $1.8 \mathrm{dl}-0.3 \mathrm{dl}=1.5 \mathrm{dl}$ of milk and $1.2 \mathrm{dl}-0.2 \mathrm{dl}=1 \mathrm{dl}$ of coffee.

To fill the cup to the brim, $3 \mathrm{dl}-(1.5 \mathrm{dl}+1 \mathrm{dl})=0.5 \mathrm{dl}$ of liquid is still needed.

When the cup is topped up with $0.5 \mathrm{dl}$ of milk, it contains $2 \mathrm{dl}$ of milk and $1 \mathrm{dl}$ of coffee.

$\frac{1}{5}$ of $2 \mathrm{dl}$ is $0.4 \mathrm{dl}, \frac{1}{5}$ of $1 \mathrm{dl}$ is $0.2 \mathrm{dl}$.

After the second sip, the cup contains $2 \mathrm{dl}-0.4 \mathrm{dl}=1.6 \mathrm{dl}$ of milk and $1 \mathrm{dl}-0.2 \mathrm{dl}=0.8 \mathrm{dl}$ of coffee.

To fill the cup to the brim, $3 \mathrm{dl}-(1.6 \mathrm{dl}+0.8 \mathrm{dl})=0.6 \mathrm{dl}$ of liquid is still needed.

Since five times more milk than coffee is poured into the cup, this means that $0.5 \mathrm{dl}$ of milk and $0.1 \mathrm{dl}$ of coffee are added. After topping up, the cup contains $2.1 \mathrm{dl}$ of milk and $0.9 \mathrm{dl}$ of coffee.

If the cup is filled to one-third with white coffee, this means that $\frac{2}{3}$ of the white coffee has been drunk, while $\frac{1}{3}$ remains in the cup.

$\frac{1}{3}$ of $2.1 \mathrm{dl}$ is $0.7 \mathrm{dl}, \frac{1}{3}$ of $0.9 \mathrm{dl}$ is $0.3 \mathrm{dl}$.

After the third sip, the cup contains $0.7 \mathrm{dl}$ of milk and $0.3 \mathrm{dl}$ of coffee. Thus, there is $1 \mathrm{dl}$ of white coffee in the cup, and 2 dl of milk needs to be added to fill the cup.

After adding the milk, the cup will contain $0.7 \mathrm{dl}+2 \mathrm{dl}=2.7 \mathrm{dl}$ of milk.