A drum contains 165 litres of ethanol. 44 litres of this liquid is removed and replaced with water. 44 litres of this mixture is again removed and replaced with water. How much water (in litres) is present in this drum now?

Options

A. 80.55
B. 88.73
C. 76.26
D. 71.66

Answer

To solve the problem step by step, we will follow the process of removing ethanol and replacing it with water, and then repeat the process.

### Step 1: Initial Setup
- The drum contains **165 liters** of ethanol.

### Step 2: First Removal and Replacement
- We remove **44 liters** of ethanol.
- Remaining ethanol = 165 liters - 44 liters = **121 liters**.
- We add **44 liters** of water.
- Total volume in the drum remains **165 liters** (121 liters of ethanol + 44 liters of water).

### Step 3: Second Removal and Replacement
- Now, we need to find the concentration of ethanol in the mixture before the second removal.
- The total mixture is 165 liters, with **121 liters** of ethanol and **44 liters** of water.
- The fraction of ethanol in the mixture = \( \frac{121}{165} \).
- When we remove **44 liters** of this mixture, the amount of ethanol removed is:
\[ \text{Ethanol removed} = 44 \times \frac{121}{165} = \frac{44 \times 121}{165} = \frac{5324}{165} \approx 32.3 \text{ liters} \]
- Remaining ethanol after the second removal:
\[ \text{Remaining ethanol} = 121 - 32.3 \approx 88.7 \text{ liters} \]
- We add **44 liters** of water again.
- Total volume in the drum remains **165 liters** (88.7 liters of ethanol + 44 liters of water).

### Step 4: Calculate Final Amount of Water
- The total amount of water in the drum now:
\[ \text{Total water} = 44 \text{ liters (added)} + 44 \text{ liters (from the first replacement)} = 88 \text{ liters} \]

### Step 5: Final Calculation
- The total volume of the drum is still **165 liters**.
- The remaining ethanol is approximately **88.7 liters**.
- Thus, the final amount of water in the drum:
\[ \text{Water} = 165 - 88.7 \approx 76.3 \text{ liters} \]

### Conclusion
The total amount of water present in the drum now is approximately **76.3 liters**.

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