This GRE Math practice problem tests your understanding of mixtures and fractions.

Two $600$ ml pitchers contain orange juice. One pitcher is $\frac{1}{3}$ full and the other pitcher is $\frac{2}{5}$ full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?

- $\quad \dfrac{1}{8}$
- $\quad \dfrac{3}{16}$
- $\quad \dfrac{11}{30}$
- $\quad \dfrac{11}{19}$
- $\quad \dfrac{11}{15}$

(Source: 2004 AMC 8)

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