Multiple choice

Find the correct relationship between the given quantities: Quantity I: Quantity of petrol in the new mixture, if 50L pure petrol is mixed with kerosene by replacing 4L of petrol with kerosene thrice. Quantity II: Quantity of milk left in the new solution, if 45L of pure milk is mixed with water by replacing 3L of milk with water twice.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
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A Correct answer
Explanation

Quantity I: 50L petrol. Each operation: remove 4L petrol, add 4L kerosene. After 3 operations: 50 × (46/50)^3 = 50 × 0.92^3 = 50 × 0.778688 = 38.93L petrol. Quantity II: 45L milk. Each operation: remove 3L milk, add 3L water. After 2 operations: 45 × (42/45)^2 = 45 × (14/15)^2 = 45 × 196/225 = 39.2L milk. Since 39.2 > 38.9, Quantity II > Quantity I.

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