Successive replacement in an 80 L ethanol tank: Remove 20 L and replace with water, repeat once more. How much water is now in the tank?

Introduction / Context:We start with pure ethanol and repeatedly remove a fixed volume and replace with water. After two operations, compute ethanol remaining then infer water.

Given Data / Assumptions:

• Total V = 80 L; draw d = 20 L; n = 2 operations.
• Initially, 100% ethanol.

Concept / Approach:Remaining ethanol = V*(1 − d/V)^n = 80*(1 − 20/80)^2 = 80*(3/4)^2.

Step-by-Step Solution:

Verification / Alternative check:Sequential: after first step ethanol = 60 L; after second, remove 1/4 of the 60 (15), leaving 45 → water 35.

Why Other Options Are Wrong:40 and 44 misapply single-step removal; 45 is ethanol, not water.

Common Pitfalls:Reporting remaining ethanol instead of the asked water volume.

Final Answer:35