A drum contains 80 litres of ethanol initially. If 20 litres of the liquid is removed and replaced with water, and then again 20 litres of the resulting mixture is removed and replaced with water, how many litres of water are present in the drum now?

Introduction:
This is a two-step replacement (dilution) problem. The drum starts with pure ethanol. When we remove 20 litres and replace with water, the ethanol concentration decreases. In the second replacement, we remove a mixture (not pure ethanol), so we remove some ethanol and some water, and then add water again. The goal is to calculate how much water accumulates in the drum after two such operations. The safest approach is to track ethanol and water amounts after each step.

Given Data / Assumptions:

• Initial total volume = 80 litres• Initially: ethanol = 80 L, water = 0 L• Each operation: remove 20 L and replace with 20 L water• Number of operations = 2

Concept / Approach:
After each removal, the removed portion has the same composition as the drum at that moment. So we compute the ethanol and water removed based on current fractions, subtract them, and then add water replacement. After two operations, read the water amount.

Step-by-Step Solution:
Step 1: After first removal (from pure ethanol).Remove 20 L ethanol, remaining ethanol = 80 - 20 = 60 LAdd 20 L water, so water = 20 LAfter step 1: ethanol = 60 L, water = 20 LStep 2: Find composition before second removal.Total = 80 L, ethanol fraction = 60/80 = 3/4, water fraction = 20/80 = 1/4Step 3: Remove 20 L of mixture in step 2.Ethanol removed = 20*(3/4)=15 LWater removed = 20*(1/4)=5 LRemaining ethanol = 60 - 15 = 45 LRemaining water = 20 - 5 = 15 LStep 4: Replace removed 20 L with water.Water becomes 15 + 20 = 35 LFinal: ethanol = 45 L, water = 35 L

Verification / Alternative check:
Total volume remains 80 L throughout (because we remove 20 and add 20). Final ethanol + water = 45 + 35 = 80, consistent. Also, water must be less than 40 here because the second removal removed some water too (5 L), which prevents water from reaching 40. This sanity check matches the computed 35 L.

Why Other Options Are Wrong:
40 assumes no water was removed in the second step, which is incorrect.44 and 45 are impossible because total water cannot exceed 80 and two-step dilution here does not add that much net water.30 is too low; even after removing some water, a significant amount is added twice.

Common Pitfalls:
• Assuming the second 20 L removed is pure ethanol.• Forgetting that some water is removed in the second operation.• Not tracking volumes after each step and jumping to a wrong shortcut.

Final Answer:
The amount of water present in the drum after two replacements is 35 litres.