Discussion
A pot contains 40 liters of juice. How much juice will be there in the pot, if 4 liters of juice was removed and was replaced by water and this process was further repeated twice?
Answer: D
When a fraction of a solution is repeatedly removed and replaced, the original liquid left after \( n \) operations is
\[ A\left(1 - \frac{x}{A}\right)^{n} \]
Here \( A = 40 \), \( x = 4 \) and \( n = 3 \) (once, then twice more):
\[ 40\left(1 - \frac{4}{40}\right)^{3} = 40(0.9)^{3} \]
\[ = 40 \times 0.729 = 29.16 \text{ litres} \]
Simply subtracting \( 3 \times 4 = 12 \) litres would give 28, but each later removal takes out some water as well as juice.
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