A container has 50 litres of milk. A process is repeated three times: (1) Remove 5 litres of the current mixture from the container. (2) Replace the removed 5 litres by adding 5 litres of water. After performing this remove-and-replace process 3 times, how many litres of milk will be left in the container (assume perfect mixing each time)?

Introduction / Context:This is a repeated replacement (successive dilution) question. Each time you remove some volume from a well-mixed container and replace it with water, the remaining amount of milk is multiplied by a constant factor. The process is exponential, not linear, because after the first replacement the removed liquid is no longer pure milk.

Given Data / Assumptions:

• Initial milk = 50 L (pure)
• Each time removed = 5 L
• Each time replaced with = 5 L water
• Number of repetitions = 3
• Mixture is perfectly mixed before each removal

Concept / Approach:Milk left after n operations = initial milk * (1 - removed/total)^n. Here removed/total = 5/50 = 0.1, so remaining factor is 0.9 each time.

Step-by-Step Solution:

Verification / Alternative check:After each operation milk must decrease. Starting at 50 L, after 1st: 45 L, after 2nd: 40.5 L, after 3rd: 36.45 L. The decreasing sequence is consistent and confirms exponential reduction.

Why Other Options Are Wrong:

Common Pitfalls:Do not subtract 5 L of milk each time (50 - 15 = 35) because later removals are mixed. Also, do not forget the “perfect mixing” assumption; without mixing, the calculation changes, but here it is explicitly a mixture replacement model.

Final Answer:36.45 L