A fruit seller is sells fruit juice costing RS 24 per litre. In what ratio of water is mixed so that juice would be worth of RS 20 per litre?

1. A

   1:4

2. B

   1:5

3. C

   1:6

4. D

   2:5

Appeared in: RML Lucknow - 2021

Explanation

• The problem requires finding the ratio of a cheaper item (water at Rs 0/L) to a dearer item (juice at Rs 24/L) to create a mixture with a mean price (Rs 20/L).
• The rule of alligation is the most direct method for this calculation.
• The quantity of the cheaper item (water) is proportional to the difference between the dearer price and the mean price (24 - 20 = 4).
• The quantity of the dearer item (juice) is proportional to the difference between the mean price and the cheaper price (20 - 0 = 20).
• This gives a ratio of water to juice as 4:20.
• Simplifying the ratio 4:20 by dividing both parts by 4 results in the final ratio of 1:5.

Why Other Options Were Wrong

• Option A: A ratio of 1:4 is incorrect. This might result from a calculation error, such as incorrectly calculating the difference (e.g., 24-20=4 and 20-4=16, leading to 4:16 or 1:4).
• Option C: A ratio of 1:6 is incorrect. This could arise from miscalculating the difference for the juice part, for instance, using the juice's original price (24) instead of the difference (20), leading to a ratio of 4:24 or 1:6.
• Option D: A ratio of 2:5 is incorrect. This is the simplified form of 8:20, not 4:20. It might result from an arithmetic error in the initial subtraction step.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mixture and Alligation as background academic context rather than a clinical decision trigger.
• This question tests general quantitative aptitude, a skill necessary for nurses for tasks like medication dosage calculations, fluid balance charting, and interpreting various numerical data in a clinical setting.
• While not a direct clinical scenario, the underlying mathematical reasoning is crucial for patient safety and effective care.
• What if the cost of juice was Rs 30 and the target price was Rs 25? The ratio of water to juice would be (30-25) : (25-0) = 5:25, which simplifies to 1:5. The logic remains the same.

How to Approach the Question

• First, identify the question as a mixture problem where two items of different values are combined to create a mixture of a specific intermediate value.
• Identify the values of the two components being mixed. Here, it's juice at Rs 24/L and water, which is assumed to have a value of Rs 0/L.
• Note the desired 'mean' value of the final mixture, which is Rs 20/L.
• Apply the rule of alligation. Place the cheaper value (0) on the left, the dearer value (24) on the right, and the mean value (20) in the middle.
• Subtract the mean value from the dearer value (24 - 20 = 4). This number represents the 'part' of the cheaper item (water).
• Subtract the cheaper value from the mean value (20 - 0 = 20). This number represents the 'part' of the dearer item (juice).

Concept Tested & Keywords

• Concept Tested: Mixture and Alligation
• Stem keywords: fruit juice, costing, Rs 24 per litre, ratio, water, Rs 20 per litre
• Lead-in keywords: In what ratio

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