Discussion
A container contains 30 liters of milk. From this container 5 liter 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: C
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 \( A = 30 \), \( x = 5 \) and \( n = 3 \):
\[ 30\left(1 - \frac{5}{30}\right)^{3} = 30\left(\frac{5}{6}\right)^{3} \]
\[ = 30 \times \frac{125}{216} = 17.36 \text{ litres} \]
Subtracting \( 3 \times 5 = 15 \) litres would give 15 L, but the later withdrawals remove water as well as milk, so more milk survives than that.
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