An item is sold for Rs. x at a 10% loss. If the same item is sold for Rs. y, there is an 18% profit. What is the ratio of (2x+y) : (2x-y)?

1. A

   118:45

2. B

   59:45

3. C

   153:35

4. D

   149:31

Appeared in: CGHS SSC - 2018

Explanation

• The problem requires expressing the two selling prices, x (at a 10% loss) and y (at an 18% profit), in terms of a common Cost Price (CP).
• Let the CP be C. Then the selling price at a 10% loss is x = 0.90C, and the selling price at an 18% profit is y = 1.18C.
• Substitute these values into the expression (2x + y) : (2x - y), which gives (2 * 0.90C + 1.18C) : (2 * 0.90C - 1.18C).
• The expression simplifies to (1.80C + 1.18C) : (1.80C - 1.18C), which is 2.98C : 0.62C.
• After canceling C and removing decimals (multiplying by 100), the ratio becomes 298 : 62.
• Dividing both sides by 2 gives the final simplified ratio of 149:31.

Why Other Options Were Wrong

• Option A: This ratio is incorrect. It may result from calculation errors, such as incorrectly adding or subtracting the decimal values in the numerator and denominator.
• Option B: This ratio is incorrect. It might arise from a miscalculation, perhaps by simplifying one part of the ratio incorrectly or making an error in the initial setup.
• Option C: This ratio is arithmetically incorrect. It does not stem from the correct substitution and simplification of the expressions for x and y.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss, Ratio and Proportion as background academic context rather than a clinical decision trigger.
• This is a quantitative aptitude question designed to test mathematical reasoning and problem-solving skills, which are not directly clinical but are essential for analytical thinking.
• Skills in calculating percentages and ratios are valuable in nursing management and administration, particularly for tasks related to budgeting, resource allocation, and staffing.
• What if the loss was 20% and the profit was 10%? Then x = 0.8C and y = 1.1C. The ratio (2x+y) : (2x-y) would be (1.6C + 1.1C) : (1.6C - 1.1C) = 2.7C : 0.5C = 27:5.

How to Approach the Question

• First, identify the key concepts in the question: profit, loss, and ratio.
• Establish a base value. Let the unknown Cost Price (CP) be a variable, such as 'C' or '100'.
• Translate the percentage loss into an equation for selling price 'x'. A 10% loss means x = (100% - 10%) of CP, so x = 0.90 * CP.
• Translate the percentage profit into an equation for selling price 'y'. An 18% profit means y = (100% + 18%) of CP, so y = 1.18 * CP.
• Substitute these algebraic expressions for 'x' and 'y' into the target ratio given in the question: (2x + y) : (2x - y).
• Perform the algebraic simplification. The 'CP' variable should cancel out from the numerator and denominator.

Concept Tested & Keywords

• Concept Tested: Profit and Loss, Ratio and Proportion
• Stem keywords: item sold, loss, profit, ratio
• Lead-in keywords: What is the ratio

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