Question : A container contains 25 litres of milk. From this container, 5 litres of milk is taken out and replaced by water. This process is further repeated two times. How much milk is there in the container now?
Option 1: 11.5 litres
Option 2: 14.8 litres
Option 3: 13.5 litres
Option 4: 12.8 litres
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Correct Answer: 12.8 litres
Solution : Left quantity = Initial quantity(1 – [Fraction removed]) N (Where N = Number of times the process is carried out) Fraction of milk removed = $\frac{5}{25}$ = $\frac{1}{5}$ Now, the quantity of milk left in the container $= 25(1 - \frac{1}{5})^3$ $= 25 × (\frac{4}{5})^3$ $= 25 × \frac{64}{125}$ $= 12.8$ litres ∴ There are 12.8 litres of milk left in the container. Hence, the correct answer is 12.8 litres.
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