Discussion
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Answer: D
When a fraction of a solution is repeatedly removed and replaced, the original liquid left after \( n \) operations is
\[ A\left(1 - \frac{x}{A}\right)^{n} \]
With \( A = 40 \), \( x = 4 \) and \( n = 3 \):
\[ 40(0.9)^{3} = 40 \times 0.729 = 29.16 \text{ litres} \]
Each operation leaves 90% of the milk then present, and three such reductions compound rather than add.
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