2. There are already several red and black balls in the box. After adding some black balls, the red balls account for one quarter of the total number of balls; after adding some more red balls, the number of red balls is two-thirds of the black balls. If the number of black balls and red balls added is the same, then the original ratio of black balls to red balls in the box is . $\qquad$
【Answer】 $2: 1$
【Analysis】Let the initial number of black balls and red balls be $a$ and $b$ respectively, and each time $n$ balls are added;
Then we have: $\left\{\begin{array}{l}\frac{b}{a+b+n}=\frac{1}{4} \Rightarrow 4 b=a+b+n \Rightarrow n=3 b-a \\ \frac{b+n}{a+n}=\frac{2}{3} \Rightarrow 3 b+3 n=2 a+2 n \Rightarrow n=2 a-3 b\end{array} \Rightarrow 3 b-a=2 a-3 b \Rightarrow a=2 b \Rightarrow a: b=2: 1\right.$