150 liters of mixture of milk and water contains 20% of water. How much water (In litre) must be added to it. So that there is 25% water in the new mixture?

1. A

   15

2. B

   10

3. C

   25

4. D

   20

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

• First, calculate the initial quantities: The mixture has 150 L total, with 20% water (30 L) and 80% milk (120 L).
• The core principle is that the quantity of milk (120 L) remains unchanged.
• In the new mixture, water is 25%, so milk must be 75%.
• If 120 L of milk represents 75% of the new total volume, we can calculate the new total: New Volume = 120 / 0.75 = 160 L.
• The amount of water added is the difference between the new total volume and the initial total volume: 160 L - 150 L = 10 L.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It might result from an error in calculating the new total volume or misunderstanding the relationship between the constant component (milk) and the new percentage.
• Option C: This value represents the target percentage of water (25%), not the volume of water to be added. It's a common mistake to confuse the final state's property with the change required to achieve it.
• Option D: This value represents the initial percentage of water (20%). Confusing the initial percentage with the required volume is a conceptual error.

Related Visual

• Visual 1: Diagram - A side-by-side comparison of two containers. The first container is labeled 'Initial Mixture' showing 150L divided into 120L Milk (80%) and 30L Water (20%). The second container is labeled 'Final Mixture' showing 160L divided into 120L Milk (75%) and 40L Water (25%). An arrow points from the first to the second, labeled '+10L Water'.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to solve problems involving mixtures and percentages, a key topic in quantitative aptitude as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of calculation demonstrates basic numeracy and logical reasoning skills that are essential for nurses.
• Nurses frequently perform calculations for medication dosages, IV fluid rates, and solution concentrations, which require similar mathematical aptitude.
• What if the goal was to increase the milk percentage to 90% by adding milk instead of water? You would first calculate the initial water volume (30 L). This 30 L would represent 10% of the new mixture. The new total volume would be 30 / 0.10 = 300 L. The amount of milk to add would be 300 L (new total) - 150 L (initial total) = 150 L.

How to Approach the Question

• First, read the problem carefully to identify the initial total volume and the percentages of its components.
• Calculate the absolute volume of each component in the initial mixture. (e.g., 20% of 150L is 30L of water).
• Identify the component that remains constant. In this case, only water is added, so the volume of milk stays the same.
• Determine the percentage of the constant component in the new mixture. (If water is 25%, milk is 100% - 25% = 75%).
• Use the constant volume and its new percentage to calculate the new total volume of the mixture.
• Finally, subtract the initial total volume from the new total volume to find the amount of substance that was added.

Concept Tested & Keywords

• Concept Tested: This question tests the ability to solve problems involving mixtures and percentages, a key topic in quantitative aptitude.
• Stem keywords: mixture, milk and water, liters, percentage
• Lead-in keywords: How much

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