A container is full of milk. One third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated three times. The final ratio of milk and water in the container is :

$\frac{8}{19}$

The correct answer is Option (2) → $\frac{8}{19}$

After first operation:

Amount of milk remaining = $\frac{2}{3}$

Amount of water remaining = $\frac{1}{3}$

After second operation:

Amount of milk remaining = $\frac{4}{9}$

Amount of water remaining = $\frac{5}{9}$

After Third operation:

Amount of milk remaining = $\frac{8}{27}$

Amount of water remaining = $\frac{19}{27}$

Ratio = $\frac{8}{27}×\frac{27}{19}=\frac{8}{19}$