A Jar contains 100 liters of Milk a thief stole 10 liters of Milk and replaced it with water. Next, he stole 20 liters of Milk and replaced it with water. Again he stole 25 liters of Milk and replaced with water. Then what is the quantity of water in the final mixture?a)55 Literb)54 Literc)50 Literd)46 LiterCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

According to the given data
Milk = 100*90/100*80/100*75/100 = 54
Water = 100-54 = 46

Answer

55 liter

Answer

Understanding the Problem
The jar initially contains 100 liters of milk. The thief repeatedly steals milk and replaces it with water, which dilutes the mixture over time. We will calculate the total amount of water added after each theft.
Step-by-Step Calculation
1. First Theft
- Milk Stolen: 10 liters
- Remaining Milk: 100 - 10 = 90 liters
- Water Added: 10 liters
- Total Mixture: 90 liters of milk + 10 liters of water
2. Second Theft
- Milk Stolen: 20 liters
- The ratio of milk in the mixture: 90 liters milk / 100 total liters = 0.9
- Actual Milk Stolen: 20 liters * 0.9 = 18 liters
- Remaining Milk: 90 - 18 = 72 liters
- Water Added: 20 liters
- Total Mixture: 72 liters of milk + 30 liters of water
3. Third Theft
- Milk Stolen: 25 liters
- The ratio of milk in the mixture: 72 liters milk / 102 total liters = 0.70588
- Actual Milk Stolen: 25 liters * 0.70588 = 17.647 liters
- Remaining Milk: 72 - 17.647 = 54.353 liters
- Water Added: 25 liters
- Total Mixture: 54.353 liters of milk + 55 liters of water
Final Calculation
After all the thefts and replacements, the total quantity of water in the jar is:
- Water after First Theft: 10 liters
- Water after Second Theft: 20 liters
- Water after Third Theft: 25 liters
Total Water = 10 + 20 + 25 = 55 liters
However, after the third theft, the remaining total mixture is calculated. After replacing milk with water, we find that the final amount of water in the jar is:
Total Water = 55 liters.
Therefore, the answer provided is incorrect according to the steps above, but after considering the final mixture, the amount of water is 55 liters.
The correct answer is indeed option D: 46 liters which may consider the dilution factor more directly.

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