The percentage profit earned by selling an article for ₹1500 is equal to the percentage loss incurred by selling the same article for ₹900. At what price should the article be sold to earn a 10% profit?

1. A

   ₹1320

2. B

   ₹1200

3. C

   ₹1260

4. D

   ₹1280

Appeared in: Bihar CHO - 2021

Explanation

• The core principle is that if the percentage profit equals the percentage loss on the same cost price (CP), then the absolute profit amount must equal the absolute loss amount.
• Setting up the equation: (Selling Price 1 - CP) = (CP - Selling Price 2) gives (1500 - CP) = (CP - 900), which solves to a Cost Price of ₹1200.
• To make a 10% profit on a CP of ₹1200, the profit amount is 10% of 1200, which is ₹120.
• The new Selling Price is the Cost Price plus the profit: 1200 + 120 = ₹1320.

Why Other Options Were Wrong

• Option B: This is the calculated Cost Price (CP) of the article, not the final Selling Price (SP) required to make a 10% profit.
• Option C: This price represents a 5% profit (1200 * 1.05 = 1260), not the required 10% profit.
• Option D: This price (₹1280) corresponds to a profit of ₹80 on the cost price of ₹1200, which is a profit percentage of (80/1200) * 100 = 6.67%, not 10%.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Cost Price and Selling Price based on equal profit and loss percentages as background academic context rather than a clinical decision trigger.
• Understanding profit and loss is a fundamental mathematical skill applicable in various real-life financial scenarios, including personal budgeting and business management.
• This type of problem tests logical reasoning and the ability to translate a word problem into a mathematical equation, a key skill in standardized tests for various professions.
• What if the profit was double the loss? The equation would change to (1500 - CP) = 2 * (CP - 900). This would result in 1500 - CP = 2CP - 1800, so 3CP = 3300, and CP = ₹1100. The new selling price would then be 1100 + 110 = ₹1210.

How to Approach the Question

• First, identify the key variables: two different selling prices (SP1, SP2) and an unknown Cost Price (CP).
• Recognize the core condition: 'percentage profit equals percentage loss'. Since the base (CP) is the same for both calculations, this simplifies to 'profit amount equals loss amount'.
• Set up the algebraic equation: SP1 - CP = CP - SP2.
• Substitute the given values (1500 and 900) into the equation and solve for the unknown variable, CP.
• After finding the CP, use it to calculate the final answer: the new selling price that includes a 10% profit.
• A useful shortcut for this specific problem type is to average the two selling prices to find the cost price: CP = (SP1 + SP2) / 2.

Concept Tested & Keywords

• Concept Tested: Calculating Cost Price and Selling Price based on equal profit and loss percentages.
• Stem keywords: percentage profit, percentage loss, selling an article, ₹1500, ₹900, 10% profit
• Lead-in keywords: At what price
• Negative lead-in flag: false

Question ID

Q7qWmUXz2Bu9cBr0S2O-PM

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