The list price of a dining table is ₹62,500. It is sold to a retailer after two successive discounts of 17% and 20%. The retailer wants to earn a profit of 46% on his cost after allowing a 50% discount (on its new list price) to the customer. At what price should he list the dining table?

1. A

   ₹121,099

2. B

   ₹121,180

3. C

   ₹121,271

4. D

   ₹121,136

Appeared in: DSSSB October 2024

Explanation

• First, calculate the retailer's cost price (CP) by applying the two successive discounts of 17% and 20% to the original list price: CP = ₹62,500 × (1 - 0.17) × (1 - 0.20) = ₹41,500.
• Next, determine the selling price (SP) the retailer needs to achieve a 46% profit on the cost price: SP = ₹41,500 × (1 + 0.46) = ₹60,590.
• Finally, calculate the new list price. Since the selling price of ₹60,590 is reached after a 50% discount, this SP represents 50% of the new list price.
• Therefore, the new list price is calculated as: New List Price = ₹60,590 / 0.50 = ₹121,180.

Why Other Options Were Wrong

• Option A: Incorrect. This value likely results from a miscalculation or rounding error during one of the intermediate steps, such as calculating the selling price or the final list price.
• Option C: Incorrect. This is a calculation error. It might arise from incorrectly applying the profit percentage or the final discount.
• Option D: Incorrect. This value is the result of a calculation mistake. A common error is misinterpreting how successive discounts are applied (e.g., adding them together), leading to an incorrect cost price and subsequent incorrect final price.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of profit, loss, and successive discounts as background academic context rather than a clinical decision trigger.
• While not a clinical skill, quantitative aptitude is a common component of nursing entrance and recruitment examinations in India.
• This type of problem tests logical reasoning and mathematical accuracy, which are foundational skills for tasks like medication dosage calculation and interpreting patient data.
• What if the retailer wanted to earn a 46% profit on the selling price instead of the cost? The calculation would change. The SP would represent CP + 0.46SP, so 0.54SP = CP = ₹41,500. This would make the SP = ₹76,851.85, and the new list price would be ₹153,703.70.

How to Approach the Question

• First, identify all the given values: original list price, two successive discounts for the retailer, the retailer's profit margin, and the final discount for the customer.
• Break the problem into three main steps: 1. Calculate the retailer's actual cost price. 2. Calculate the retailer's target selling price. 3. Calculate the new list price the retailer must set.
• For Step 1, remember that successive discounts are applied one after another on the reduced price, not added together. Calculate CP = Original Price × (1 - d1%) × (1 - d2%).
• For Step 2, calculate the target selling price by adding the desired profit to the cost price: SP = CP × (1 + profit%).
• For Step 3, work backward from the selling price. The SP is the price after the final 50% discount. So, New List Price = SP / (1 - final discount%).
• Perform each calculation carefully to avoid errors, as a mistake in an early step will affect the final result.

Concept Tested & Keywords

• Concept Tested: Calculation of profit, loss, and successive discounts.
• Stem keywords: list price, dining table, successive discounts, retailer, profit, cost, discount
• Lead-in keywords: At what price

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