From a container full of orange juice, 7.5 liters was drawn out and replaced by soda water. This process is repeated 5 more times. 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 \((0.44)^{1/6} = 0.802\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 37.9 litres
Let the container hold V litres. Each time 7.5 litres is drawn out and replaced, the fraction of juice left is multiplied by \(\left(1 - \frac{7.5}{V}\right)\).
The process is done once and repeated 5 more times, so 6 times in all:
\( \displaystyle \text{Juice left} = V\left(1 - \frac{7.5}{V}\right)^6 \)
Juice : soda = 4 : 5, so juice is \(\frac{4}{9} \approx 0.44\) of the container:
\( \displaystyle \left(1 - \frac{7.5}{V}\right)^6 = 0.44 \)
\( \displaystyle 1 - \frac{7.5}{V} = (0.44)^{1/6} = 0.802 \) (given)
\( \displaystyle \frac{7.5}{V} = 0.198 \)
\( \displaystyle V = \frac{7.5}{0.198} \approx 37.9 \) litres