A fruit seller sells fruit juice costing Rs. 24 per litre. In what ratio should water be mixed so that the resulting mixture costs Rs. 20 per litre?

1. A

   1:4

2. B

   1:5

3. C

   1:6

4. D

   2:5

Appeared in: RML 2023

Explanation

• This is a classic problem solved using the Rule of Alligation, a method to find the ratio in which two ingredients at given prices must be mixed to produce a mixture of a desired price.
• The cost of the cheaper ingredient (water) is taken as Rs. 0, and the cost of the dearer ingredient (fruit juice) is Rs. 24 per litre.
• The desired mean price of the mixture is Rs. 20 per litre.
• The ratio of Water to Juice is calculated as (Price of Dearer - Mean Price) : (Mean Price - Price of Cheaper).
• Calculation: (24 - 20) : (20 - 0) = 4 : 20, which simplifies to 1:5.

Why Other Options Were Wrong

• Option A: If water and juice are mixed in a 1:4 ratio, the total cost for 5 litres would be (10 + 424) = Rs. 96. The price per litre would be 96/5 = Rs. 19.20, not Rs. 20.
• Option C: If mixed in a 1:6 ratio, the total cost for 7 litres is (10 + 624) = Rs. 144. The price per litre would be 144/7 ≈ Rs. 20.57, not Rs. 20.
• Option D: If mixed in a 2:5 ratio, the total cost for 7 litres is (20 + 524) = Rs. 120. The price per litre would be 120/7 ≈ Rs. 17.14, not Rs. 20.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Rule of Alligation in Mixtures as background academic context rather than a clinical decision trigger.
• Understanding ratios and proportions is a fundamental mathematical skill essential for various calculations in daily life and professional settings, including dosage calculations in nursing.
• The Rule of Alligation is a shortcut technique that simplifies solving problems involving mixtures, saving time in competitive exams.
• What if the desired price was Rs. 22 per litre? The ratio would change to (24-22) : (22-0) = 2 : 22 = 1:11, showing how the ratio depends directly on the target price.

How to Approach the Question

• Identify the problem as a mixture problem where two ingredients are mixed to get a mixture with a specific property (in this case, price).
• Recognize that the Rule of Alligation is the most efficient method to solve this.
• List the values: Cost of cheaper ingredient (water = 0), cost of dearer ingredient (juice = 24), and the mean price (mixture = 20).
• Apply the alligation formula: (Quantity of cheaper) / (Quantity of dearer) = (Price of dearer - Mean price) / (Mean price - Price of cheaper).
• Calculate the differences and form the ratio: (24 - 20) : (20 - 0) = 4 : 20.
• Simplify the resulting ratio to its lowest terms (1:5) and match it with the given options.

Concept Tested & Keywords

• Concept Tested: Rule of Alligation in Mixtures
• Stem keywords: fruit juice, cost, water, mixture, ratio
• Lead-in keywords: In what ratio
• Negative lead-in flag: false

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