A 40-litre container of milk has 4 litres removed and replaced by water, and this operation is repeated twice more. How much milk remains?

Problem restatementSuccessive replacement: each time remove 4 L of the current mixture from a 40 L container (initially pure milk) and refill with water. After 3 such operations, find remaining milk.

Given data

• Initial milk = 40 L; each cycle removes 4 L and replaces with water.
• Number of cycles n = 3.

Concept/ApproachUse the standard successive-replacement formula: Remaining milk = Initial × (1 − removed/total)ⁿ.

Step-by-step calculation Remaining milk = 40 × (1 − 4/40)³ = 40 × (36/40)³ = 40 × (0.9)³ = 40 × 0.729 = 29.16 L

Verification/AlternativeIterative check: After 1st cycle milk = 40×0.9 = 36; 2nd = 36×0.9 = 32.4; 3rd = 32.4×0.9 = 29.16 L.

Common pitfalls

• Subtracting 12 L instead of compounding proportions (replacement is proportional, not absolute).

Final Answer29.16 litres