Multiple choice

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship among them. Find the quantity of water in final solution. Quantity I: When 72 liter water is added in the solution percentage of milk is reduced from 36% to 21%. Quantity II: A container contains 48 liter pure milk. From this 9.6 liter mixture is taken out and replaced with water. This process is repeated one more time.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established

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A Correct answer
Explanation

Quantity I: Let initial solution volume = V, with 36% milk. Milk = 0.36V, water = 0.64V. After adding 72L water: milk % = 21%, so 0.36V / (V+72) = 0.21. Solving: 0.36V = 0.21V + 15.12, so 0.15V = 15.12, V = 100.8. Final water = 0.64(100.8) + 72 = 64.512 + 72 = 136.512 L. Quantity II: Initial milk = 48L. First replacement: remove 9.6L mixture (20% of 48), so milk removed = 9.6 × (48/48) = 9.6L, remaining milk = 48 - 9.6 = 38.4L. After adding water: mixture = 48L (38.4 milk + 9.6 water). Second replacement: remove 9.6L mixture, milk removed = 9.6 × (38.4/48) = 7.68L, remaining milk = 38.4 - 7.68 = 30.72L. Final water = 48 - 30.72 = 17.28L. Since 136.512 > 17.28, Quantity I > Quantity II.