A container is full of mango juice. One fifth of juice is taken out from this container and then an equal amount of water is poured into the bottle. This process is repeated 3 more times. The final ratio of juice and water in the container is :

$\frac{256}{369}$

The correct answer is Option (3) → $\frac{256}{369}$

Remaining juice formula = $\left(1-\frac{1}{5}\right)^n$

when $n=4$,

Remaining juice = $\left(\frac{4}{5}\right)^4$

∴ Water fraction = $1-\left(\frac{4}{5}\right)^4=\frac{369}{625}$

∴ The ratio of mango juice : water is, $256:369$