To produce the first quality of paint, two types of chemicals C3 and C4 are mixed in the ratio 3:5. If the same chemicals are mixed in the ratio 2:3, a second quality of paint is obtained. How many liters of the first quality paint should be mixed with 15 liters of the second quality paint so that a third quality paint with the two varieties in the ratio 8:13 can be produced?

1. A

   28

2. B

   38

3. C

   48

4. D

   58

Appeared in: Haryana CHO - 2022

Explanation

• The problem is solved by focusing on the proportion of a single component (chemical C3) across the different mixtures.
• The amount of C3 in the first quality paint is represented as (3/8)x, where x is the unknown volume.
• The amount of C3 in the second quality paint is calculated as (2/5) of 15 liters, which is 6 liters.
• An equation is set up where the total amount of C3, [(3x/8) + 6], divided by the total volume, [x + 15], equals the final desired proportion of C3, which is 8/21.
• Solving the algebraic equation ((3x/8) + 6) / (x + 15) = 8/21 yields x = 48.

Why Other Options Were Wrong

• Option A: This is an incorrect result, likely due to an arithmetic error during the cross-multiplication or simplification steps of the equation.
• Option B: This value is incorrect and would arise from a miscalculation, such as an error in combining terms or isolating the variable 'x'.
• Option D: This is an incorrect answer. An error such as incorrectly calculating the initial amount of C3 in the 15-liter solution or a mistake in solving the final algebraic step could lead to this result.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mixtures and Alligations as background academic context rather than a clinical decision trigger.
• The mathematical principle of ratio and proportion is a critical skill in nursing for ensuring patient safety and treatment efficacy.
• It is fundamental for accurate medication dosage calculations, where nurses must determine the correct volume of a drug to administer based on the stock concentration (e.g., mg/mL).
• This concept is also applied when calculating IV drip rates (gtt/min) and reconstituting powdered medications.

How to Approach the Question

• First, break down the problem by identifying the components and their ratios in each solution.
• Choose one component to track consistently throughout the problem (in this case, chemical C3).
• Express the proportion of this chosen component in each solution as a fraction (e.g., C3 in the first paint is 3/8).
• Let 'x' be the unknown volume. Write expressions for the amount of the component in each part of the mixture.
• Set up an equation: (Total amount of the component in the mixture) / (Total volume of the mixture) = (Final proportion of the component).
• Solve the resulting algebraic equation for 'x' to find the unknown volume.

Concept Tested & Keywords

• Concept Tested: Mixtures and Alligations
• Stem keywords: paint, chemicals, mixed, ratio
• Lead-in keywords: How many liters

Question ID

QYR6JcrLtBaFw42bX8pVKw

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