Discussion
A drum contains forty liters of whisky. Four liters of whisky is taken out and replaced by soda. This process is carried out twice further. How much whisky is now contained by the container?
Answer: B
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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