In what ratio should sugar costing ₹52.5 per kg be mixed with sugar costing ₹17 per kg so that there is a profit of 12% on selling the mixture at ₹44.8 per kg?

1. A

   46 : 25

2. B

   24 : 49

3. C

   27 : 41

4. D

   27 : 48

Appeared in: DSSSB 6 September 2024

Explanation

• First, calculate the cost price (CP) of the mixture using the selling price (SP) and profit percentage. The formula is CP = SP / (1 + Profit%/100).
• Given SP = ₹44.8 and Profit = 12%, the CP = 44.8 / 1.12 = ₹40 per kg.
• Next, apply the rule of alligation. This rule helps find the ratio of two ingredients when their individual costs and the mean cost of the mixture are known.
• The ratio of the dearer sugar (costing ₹52.5) to the cheaper sugar (costing ₹17) is calculated as (Mean Price - Cheaper Price) : (Dearer Price - Mean Price).
• Substituting the values: (40 - 17) : (52.5 - 40) = 23 : 12.5.
• To convert this to a whole number ratio, multiply both sides by 2, which gives 46 : 25.

Why Other Options Were Wrong

• Option B: This ratio is incorrect. It may result from a miscalculation in the alligation step or an error in calculating the cost price of the mixture.
• Option C: This ratio is incorrect. It likely arises from calculation errors, such as incorrectly subtracting the values in the alligation formula.
• Option D: This ratio is incorrect. Such a result could occur if the selling price was mistakenly used as the mean price in the alligation rule, or from other arithmetic mistakes.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mixtures and Alligation with Profit Percentage as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a skill essential for various competitive examinations, including those for nursing positions.
• The ability to solve problems involving percentages, ratios, and mixtures is a measure of logical reasoning and analytical skills.
• What if the mixture was sold at a loss of 10% instead of a profit? The cost price would be calculated as CP = 44.8 / (1 - 0.10) = 44.8 / 0.90 ≈ ₹49.78. This new CP would then be used in the alligation formula, leading to a different ratio.

How to Approach the Question

• First, identify all the given values: the cost of the two types of sugar, the selling price of the mixture, and the profit percentage.
• Recognize that the 'mean price' required for the alligation rule is the cost price (CP) of the mixture, not the selling price (SP).
• Calculate the CP of the mixture by removing the profit from the SP using the formula: CP = SP / (1 + Profit%/100).
• Set up the alligation diagram with the cost of the dearer item on one side, the cheaper item on the other, and the calculated mean price (CP) in the middle.
• Perform the cross-subtraction: subtract the cheaper cost from the mean price, and subtract the mean price from the dearer cost.
• The two results from the subtraction give the required ratio. Simplify the ratio to its simplest whole number form if necessary.

Concept Tested & Keywords

• Concept Tested: Mixtures and Alligation with Profit Percentage
• Stem keywords: ratio, sugar, costing, mixed, profit, selling mixture
• Lead-in keywords: In what ratio

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