$1 \cdot 112$ In cup A, there are $m$ milliliters of red ink, and in cup B, there are $m$ milliliters of blue ink. Pour $a$ milliliters from cup A to cup B $(0<a<m)$, stir it, and then pour $a$ milliliters from cup B back to cup A, then at this moment,
(A) The blue ink mixed into cup A is less than the red ink mixed into cup B.
(B) The blue ink mixed into cup A is more than the red ink mixed into cup B.
(C) The blue ink mixed into cup A is the same as the red ink mixed into cup B.
(D) The relationship between the amount of blue ink mixed into cup A and the amount of red ink mixed into cup B is uncertain.
(1st "Hope Cup" National Mathematics Invitational Competition, 1990)
[Solution] According to the problem, after pouring $a$ milliliters from cup A to cup B, the concentrations of red and blue ink in cup B are
$$
\frac{a}{m+a}, \quad \frac{m}{m+a}.
$$

After mixing, when $a$ milliliters are taken from cup B and poured back into cup A, the amount of blue ink (i.e., the blue ink mixed into cup A) is $\frac{m a}{m+a}$;
while the remaining ink in cup B contains red ink as
$$
a-\frac{a}{m+a} \cdot a=\frac{m a}{m+a} \text{. }
$$

Thus, the two amounts are equal.
Therefore, the correct choice is $(C)$.