Multiple choice

Passage

Directions: Study the information carefully and answer the question that follows. A right circular conical vessel was filled with milk and water in the ratio 3 : 7. If x ml of mixture was sold and replaced with x ml of pure milk, the ratio of milk to water in the final mixture becomes 51 : 49. The quantity of mixture sold is 70 ml less than the initial quantity of mixture in the vessel.

Find the quantity of water in the final mixture.

  1. 49 ml

  2. 50 ml

  3. 63 ml

  4. 65.200 ml

  5. 67.400 ml
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A Correct answer
Explanation

Initial ratio 3:7. After replacing x ml, the ratio becomes 51:49. The total volume remains constant. Let initial volume be V. The amount of water changes from 0.7V to 0.7(V-x) = 0.49(V). Thus 0.7V - 0.7x = 0.49V, so 0.21V = 0.7x, x = 0.3V. Also, x = V - 70. So 0.3V = V - 70, 0.7V = 70, V = 100. Final mixture volume is 100. Water = 0.49 * 100 = 49 ml.

AI explanation

Let the initial mixture be V. Since x is 70 ml less than V, V = x + 70. The initial water fraction is 7/10, and the final water fraction is 49/100. Using the replacement formula for water: (7/10) * ((x + 70 - x) / (x + 70))^2 = 49/100. This simplifies to (7/10) * (70 / (x + 70))^2 = 49/100. Solving yields x + 70 = 100, making the final total mixture 100 ml. The final quantity of water is 49% of 100, which equals 49 ml.

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