A person incurs 20% loss by selling an article for ₹ 480. At what price must he sell to earn 20% profit?

Appeared in: UPPSC 2017

Explanation

The first step is to determine the original cost price (CP) of the article. Since it was sold for ₹ 480 at a 20% loss, the selling price represents 80% of the CP.
Using the formula CP = (Selling Price × 100) / (100 - Loss %), the cost price is calculated as (480 × 100) / 80, which equals ₹ 600.
The next step is to calculate the new selling price (SP) that will yield a 20% profit on the cost price of ₹ 600.
Using the formula New SP = CP × (100 + Profit %) / 100, the new selling price is (600 × 120) / 100, which equals ₹ 720.

Option A: Selling at ₹ 680 would result in a profit of ₹ 80 (₹ 680 - ₹ 600). This corresponds to a profit percentage of (80/600) × 100 = 13.33%, which is less than the desired 20%.
Option B: Selling at ₹ 700 would result in a profit of ₹ 100 (₹ 700 - ₹ 600). This corresponds to a profit percentage of (100/600) × 100 = 16.67%, which is less than the desired 20%.
Option C: Selling at ₹ 800 would result in a profit of ₹ 200 (₹ 800 - ₹ 600). This corresponds to a profit percentage of (200/600) × 100 = 33.33%, which is more than the desired 20%.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss Calculation as background academic context rather than a clinical decision trigger.
While not a clinical question, proficiency in basic mathematics is essential for nurses for tasks like medication dosage calculations, IV drip rate adjustments, and interpreting patient data.
This type of two-step problem-solving enhances analytical skills required to assess a clinical situation, identify the underlying issue (like finding the CP), and then determine the correct intervention (like calculating the new SP).
What if the initial transaction was a 20% profit instead of a loss? The initial CP would be lower (480 / 1.20 = ₹ 400), and the new selling price for a 20% profit would be ₹ 480 (400 x 1.20), which was the initial selling price.

How to Approach the Question

First, identify all the given information: the initial selling price (₹ 480) and the associated loss percentage (20%).
Recognize the goal: to find the new selling price that will result in a 20% profit.
Understand that both profit and loss are calculated based on the cost price (CP). Therefore, the first step must be to calculate the CP.
Use the formula for CP when there is a loss: CP = SP / (1 - Loss Percentage/100). This will give you the original cost of the article.
Once the CP is known, use the formula for the new SP with a desired profit: New SP = CP × (1 + Profit Percentage/100).
Calculate the final value and match it with the given options.

Concept Tested & Keywords

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