A container initially holds 50 litres of pure milk. First, 8 litres of milk are removed from the container and replaced with 8 litres of water. This process of removing 8 litres of the current mixture and replacing it with 8 litres of water is repeated two more times. After these three operations in total, how many litres of milk are now contained in the container (approximately)?

Introduction: This question is a classic repeated replacement problem where pure milk in a container is gradually replaced by water in several steps. Each time a fixed amount of the current mixture is removed and replaced with water. We must find the quantity of milk remaining after three such operations.

Given Data / Assumptions:

• Initial volume in the container = 50 litres, all milk.
• In each step, 8 litres of the current mixture are removed.
• The 8 litres removed are replaced with 8 litres of water.
• This process is repeated 3 times in total.
• The total volume in the container remains 50 litres at all times.
• We must compute the approximate volume of milk left after these 3 steps.

Concept / Approach: If V is the total volume and x litres are removed and replaced each time, the fraction of the original liquid remaining after one operation is (1 - x / V). After n identical operations, the fraction remaining is (1 - x / V)^n. Here V = 50, x = 8, and n = 3. Multiplying this fraction by 50 litres gives the milk left after three operations.

Step-by-Step Solution: Step 1: Total volume V = 50 litres, removed each time x = 8 litres. Step 2: Fraction of milk remaining after one operation = 1 - x / V = 1 - 8 / 50. Step 3: 8 / 50 = 0.16, so fraction remaining each time = 1 - 0.16 = 0.84. Step 4: After 3 operations, fraction of milk remaining = (0.84)^3. Step 5: Compute (0.84)^3 = 0.84 * 0.84 * 0.84 ≈ 0.5927. Step 6: Milk remaining = 50 * 0.5927 ≈ 29.635 litres. Step 7: Rounding to two decimal places, milk remaining ≈ 29.63 litres.

Verification / Alternative check: We can also approximate stepwise. After first operation, milk = 50 * 0.84 = 42 litres. After second operation, milk = 42 * 0.84 ≈ 35.28 litres. After third operation, milk = 35.28 * 0.84 ≈ 29.63 litres. This matches the value obtained using the direct exponential formula and confirms the result is correct.

Why Other Options Are Wrong: 24.52, 28.21, and 25.14 litres are too low compared to the calculated value and do not match the repeated 16% removal pattern correctly. 30.00 litres is close but slightly higher than the precise result; it is an overestimate and does not match the exact calculation of 29.63 litres.

Common Pitfalls: Students sometimes subtract 8 litres of milk each time, ignoring that after the first step the liquid is a mixture, not pure milk. Another mistake is to forget that the removal each time is of the current mixture in the same proportion, so a constant fraction, not a constant amount, of milk is removed. Using linear subtraction instead of an exponential fraction is a frequent source of error.

Final Answer: The container now contains approximately 29.63 litres of milk.