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A vessel is full of chocolate syrup. ¼ of the syrup is taken out of the vessel & replaced it with milk. This process is repeated 2 more times and in this process 74 ltr milk has been required. Find the total volume of solution? 
  • a)
    100 Ltr 
  • b)
    120Ltr 
  • c)
    128Ltr 
  • d)
    150Ltr 
Correct answer is option 'C'. Can you explain this answer?
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Calculation:

Step 1: Finding Initial Volume of Chocolate Syrup:
- Let the initial volume of the vessel be x liters.
- ¼ of the syrup is taken out and replaced with milk, which means ¾ of the syrup remains after the first replacement.
- After the first replacement, the volume of chocolate syrup = ¾ * x = ¾ x

Step 2: Finding Volume of Milk in the Vessel after First Replacement:
- Since 74 liters of milk is required after the final replacement, the volume of milk in the vessel after the first replacement = 74 liters.
- The volume of the vessel after the first replacement = x - ¼ x + 74 = ¾ x + 74

Step 3: Generalizing the Process:
- After each replacement, the volume of chocolate syrup reduces by ¼ of the previous volume.
- After the third replacement, the volume of chocolate syrup = ¾ x * (1 - ¼)^3 = ¾ x * ¾ * ¾ * ¾ = &frac{27}{64} x

Step 4: Solving for Total Volume of Solution:
- The total volume of the final solution = volume of chocolate syrup after the third replacement + volume of milk after the third replacement
- Total volume = &frac{27}{64} x + 74

Step 5: Equating the Total Volume with Initial Volume:
- Since the total volume remains constant throughout the process, we have:
&frac{27}{64} x + 74 = x
- Solving for x, we get x = 128 liters
Therefore, the total volume of the solution in the vessel is 128 liters, which corresponds to option c) 128 Ltr.
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A vessel is full of chocolate syrup. ¼ of the syrup is taken out of the vessel & replaced it with milk. This process is repeated 2 more times and in this process 74 ltr milk has been required. Find the total volume of solution?a)100 Ltrb)120Ltrc)128Ltrd)150LtrCorrect answer is option 'C'. Can you explain this answer?
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