From a container full of orange juice, 7.5 liters was drawn out and replaced by soda water. This process is repeated 5 more time. The ratio of quantity of orange juice and soda water left in the container is 4 : 5. How much liter of orange juice did the container originally had? (Use $(0.44)^{1/6} = 0.802$)

37.9 litres

The correct answer is Option (3) → 37.9 litres

Let the container originally have $V$ liters of orange juice.

Each time, 7.5 liters is removed and replaced by soda. Fraction of orange juice remaining each time:

$\text{Remaining fraction} = 1 - \frac{7.5}{V}$

After 6 repetitions, fraction of orange juice left:

$(1 - \frac{7.5}{V})^6$

Given ratio of orange juice to soda water is $4:5$ → fraction of orange juice:

$\frac{4}{4+5} = \frac{4}{9}$

So, $(1 - \frac{7.5}{V})^6 = \frac{4}{9} \Rightarrow 1 - \frac{7.5}{V} = (\frac{4}{9})^{1/6}$

Given $(0.44)^{1/6} = 0.802$, approximate $4/9 \approx 0.444 \approx 0.44$

$1 - \frac{7.5}{V} = 0.802 \Rightarrow \frac{7.5}{V} = 1-0.802=0.198$

$V = \frac{7.5}{0.198} \approx 37.88 \approx 38$ liters