A manufacturer sells a product to a wholesaler at a profit of 40%. The wholesaler, in turn, sells it to a retailer at a profit of 23%, and the retailer sells it to a customer at a profit of 25%. If the customer pays ₹861, find the cost price (in ₹) for the manufacturer.

1. A

   401

2. B

   400

3. C

   397

4. D

   403

Appeared in: RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Explanation

• The problem involves successive percentage increases, where each new profit is calculated on the previous selling price.
• The relationship can be modeled with the equation: Final Price = Initial Price × (1 + P₁/100) × (1 + P₂/100) × (1 + P₃/100).
• Let C be the manufacturer's cost. The equation is: 861 = C × (1 + 40/100) × (1 + 23/100) × (1 + 25/100).
• Simplifying this gives: 861 = C × 1.40 × 1.23 × 1.25.
• Solving for C: C = 861 / (1.40 × 1.23 × 1.25) = 861 / 2.1525.
• The calculation yields C = 400. Thus, the manufacturer's cost price is ₹400.

Why Other Options Were Wrong

• Option A: This value is incorrect. It likely arises from a miscalculation or an incorrect method, such as adding the percentages instead of applying them successively.
• Option C: This value is incorrect. It may result from a calculation error when dividing 861 by the combined profit multiplier.
• Option D: This value is incorrect. This could be the result of a slight miscalculation or rounding error during the intermediate steps.

Related Visual

• Visual 1: Flowchart - A flowchart illustrating the flow of the product and money from the manufacturer to the wholesaler, then to the retailer, and finally to the customer. Each arrow would be labeled with the corresponding profit percentage, showing how the price builds up at each stage.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the original cost price from a final selling price after multiple successive profit percentages have been applied as background academic context rather than a clinical decision trigger.
• This type of calculation is fundamental to business and finance for understanding pricing structures, supply chain costs, and overall profitability.
• It helps in determining the Manufacturer's Suggested Retail Price (MSRP) by accounting for the profit margins required by all parties in the distribution channel.
• What if? If the retailer's profit was 30% instead of 25%, the final price would be C × 1.40 × 1.23 × 1.30 = 2.2386C. If the customer still paid ₹861, the manufacturer's cost would have to be lower (861 / 2.2386 ≈ ₹384.61).

How to Approach the Question

• First, identify the final selling price (₹861) and the sequence of profit percentages (40%, 23%, 25%).
• Recognize that this is a successive percentage change problem. Each profit is calculated on the new, increased price, not the original cost.
• Convert each profit percentage (P%) into a decimal multiplier of the form (1 + P/100).
• Let the unknown initial value (manufacturer's cost) be 'C'. Set up the equation: C × (Multiplier 1) × (Multiplier 2) × (Multiplier 3) = Final Price.
• Substitute the values: C × 1.40 × 1.23 × 1.25 = 861.
• Isolate 'C' by dividing the final price by the product of all multipliers to find the original cost.

Concept Tested & Keywords

• Concept Tested: Calculating the original cost price from a final selling price after multiple successive profit percentages have been applied.
• Stem keywords: manufacturer, wholesaler, retailer, profit, cost price, customer pays
• Lead-in keywords: find the cost price

Question ID

Q44uKXWm9URzbX2o0g1vzH

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