A jar contains 20 litres of pure milk. First, 4 litres of milk are taken out and replaced with an equal quantity of water. Then again 4 litres of this new mixture are removed from the jar. What is the final quantity of milk left in the jar?

Introduction / Context:
This is a standard repeated replacement mixture question. It tests your understanding of how the concentration of a liquid changes when some quantity is removed and replaced with another liquid, here water, more than once.

Given Data / Assumptions:

• Initial volume in the jar = 20 litres of pure milk.• First operation: remove 4 litres of milk and add 4 litres of water.• Second operation: remove 4 litres of the resulting milk water mixture.• Total volume is always kept at 20 litres.• We must find the final amount of milk left.

Concept / Approach:
For each operation, we track the fraction of milk in the jar. When a mixture is taken out, the quantity of milk removed equals the milk fraction multiplied by the volume removed. After removing mixture, water or milk is added back to restore total volume. Repeating this process allows us to compute the new amount of milk.

Step-by-Step Solution:
Step 1: Initially milk = 20 litres, water = 0 litres.Step 2: Remove 4 litres of pure milk, so milk left = 20 − 4 = 16 litres.Step 3: Add 4 litres of water. Now total = 20 litres with 16 litres milk and 4 litres water.Step 4: Milk fraction after first operation = 16/20 = 4/5 = 0.8.Step 5: Second operation, remove 4 litres of mixture.Step 6: Milk removed this time = 0.8 * 4 = 3.2 litres.Step 7: Milk left after removal = 16 − 3.2 = 12.8 litres.Step 8: Adding back 4 litres of water only changes the water amount, not milk quantity, so milk remains 12.8 litres.

Verification / Alternative check:
We can also use the standard replacement formula: remaining quantity of milk = initial volume * (1 − withdrawn volume / total volume) raised to the number of operations. Here milk amount after two operations = 20 * (1 − 4/20)^2 = 20 * (1 − 0.2)^2 = 20 * 0.8^2 = 20 * 0.64 = 12.8 litres, matching the previous method.

Why Other Options Are Wrong:
Values 14.5, 11.6 and 10.46 litres do not correspond to the correct fraction power for two replacement steps. They may result from applying the formula only once or from arithmetic mistakes in the fractional calculations.

Common Pitfalls:
Candidates often think that exactly 8 litres of milk are removed in two steps, ignoring the fact that the second removal takes out a mixture, not pure milk. Forgetting to square the factor in the replacement formula is another frequent error.

Final Answer:
The final quantity of milk left in the jar is 12.8 litres.