How much $a \%$ alcohol should be added to $b$ liters of $c \%$ alcohol to obtain $d \%$ alcohol?
Obviously, the problem can only be solved if $d$ is the value between $a$ and $c$. Generally, $p \%$ alcohol means that in $m$ liters of solution, there is

$$
\frac{p \cdot m}{100}
$$

liters of alcohol. Thus, if $x$ liters of $a \%$ alcohol are added to $b$ liters of $c \%$ alcohol, the resulting $b+x$ liters will be $d \%$ alcohol. The alcohol content can be calculated in two ways:

$$
\frac{b c}{100}+\frac{a x}{100}=\frac{(b+x) d}{100}
$$

From this, if $d \neq a$,

$$
x=b \frac{d-c}{a-d}
$$

This gives a positive value for $x$ if $a-b$ and $d-c$ have the same sign, which precisely means that $d$ lies between $a$ and $c$.