AIIMS CRE SNO - 2023
Non-Nursing Subjects (E5)
Hard
If the cost price of 15 pens is equal to the selling price of 20 pens, then the loss percent is?
Appeared in: AIIMS CRE SNO - 2023
Explanation
- The core of the problem is the statement: Cost Price (CP) of 15 pens equals the Selling Price (SP) of 20 pens, which is written as
15 * CP = 20 * SP. - By rearranging this equation, we find the ratio
CP / SP = 20 / 15 = 4 / 3. This tells us that the cost price is equivalent to 4 parts while the selling price is 3 parts. - A loss occurs because the cost price (4 parts) is greater than the selling price (3 parts). The loss is the difference:
4 - 3 = 1part. - The loss percentage is calculated with respect to the cost price:
(Loss / CP) * 100. Plugging in the ratio values gives(1 / 4) * 100 = 25%.
Why Other Options Were Wrong
- Option B: A 20% loss is incorrect. This value might be obtained by incorrectly using the number of items sold as the base for the percentage calculation. For example, calculating the difference in quantity (20 - 15 = 5) and dividing by an incorrect base like 25,
(5/25) * 100 = 20%, is a common mistake. - Option C: A 15% loss is incorrect. This answer might be chosen by someone who incorrectly assumes the percentage is one of the numbers directly mentioned in the problem (15 pens) without performing the correct calculation.
- Option D: A 10% loss is incorrect. This is a plausible-looking percentage but does not result from the correct calculation based on the given data.
Related Visual
- Visual 1: No visuals are required for this question as it is a mathematical calculation problem.
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the understanding of profit and loss, specifically how to calculate the loss percentage when the cost and selling prices are related by quantities of goods as background academic context rather than a clinical decision trigger.
- This is a general aptitude question designed to test basic mathematical and logical reasoning skills.
- While not directly related to clinical practice, such questions are a standard part of nursing entrance and competitive exams to assess a candidate's overall analytical ability.
- What if the question stated the SP of 15 pens was equal to the CP of 20 pens? In that case,
15 * SP = 20 * CP, soSP / CP = 20 / 15 = 4 / 3. This would be a profit of 1 unit on a cost of 3 units, resulting in a profit percent of(1/3) * 100 = 33.33%.
How to Approach the Question
- First, carefully read the question to identify the relationship between cost price (CP) and selling price (SP). Here, it's
CP of 15 items = SP of 20 items. - Translate this relationship into a mathematical equation:
15 * CP = 20 * SP. - Rearrange the equation to find the ratio of CP to SP. This simplifies the problem by allowing you to work with simple numbers (e.g.,
CP/SP = 4/3). - From the ratio, determine if there is a profit (SP > CP) or a loss (CP > SP).
- Calculate the loss or profit amount using the ratio values (Loss = CP - SP).
- Finally, apply the correct formula for percentage calculation. Remember, loss or profit percentage is always calculated on the Cost Price unless specified otherwise:
Loss % = (Loss / CP) * 100.
Concept Tested & Keywords
- Concept Tested: This question tests the understanding of profit and loss, specifically how to calculate the loss percentage when the cost and selling prices are related by quantities of goods.
- Stem keywords: cost price, selling price, loss percent
- Lead-in keywords: loss percent is
Question ID
QlFCoiP7jBvk2diDk09Nu_
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