By selling 100 pens, a shopkeeper gains the selling price of 20 pens. Find his gain percent.

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The core formula for this problem is Gain Percentage = (Gain / Cost Price) × 100.
The gain is given as the selling price (SP) of 20 pens. The cost price (CP) is the SP of 100 pens minus the gain (SP of 20 pens), which equals the SP of 80 pens.
Let the SP of one pen be 'x'. The gain is 20x and the CP is 80x.
The gain percentage is calculated as (20x / 80x) * 100.
Simplifying the fraction (20/80) gives 1/4. Multiplying by 100 gives the final answer of 25%.

Option B: This value is incorrect. A gain of 30% would imply a different relationship between the gain and the cost price, which doesn't match the problem's conditions.
Option C: This value is incorrect. It does not result from the correct calculation of (20/80) * 100.
Option D: This value is incorrect. It is a common distractor close to the correct answer but is not supported by the mathematical calculation.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process: 1. Assume SP of one unit. -> 2. Calculate Total SP and Gain. -> 3. Calculate CP using the formula CP = SP - Gain. -> 4. Calculate Gain Percentage using (Gain/CP) * 100.

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.
This type of problem tests logical reasoning and mathematical aptitude, which are essential skills for nurses for tasks like medication dosage calculations, fluid balance monitoring, and interpreting data.
Accurate calculation is a fundamental skill in nursing to ensure patient safety and effective treatment.
What if the question stated the shopkeeper 'loses' the selling price of 20 pens? In that case, it would be a loss calculation. The Cost Price would be SP + Loss = 100x + 20x = 120x. The Loss % would be (20x / 120x) * 100 = 16.67%.

How to Approach the Question

First, carefully read the question to understand what is given: the number of items sold and how the gain is defined (in terms of the selling price of a certain number of items).
To simplify the problem, assume a convenient value for the selling price (SP) of one item, such as Re. 1 or 'x'.
Calculate the total SP for all items sold and the total gain based on the assumed SP.
Use the fundamental relationship: Cost Price (CP) = Selling Price (SP) - Gain to find the total CP.
Apply the formula for gain percentage: Gain % = (Gain / CP) × 100.
Perform the calculation and compare your result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Profit and Loss Calculation
Stem keywords: selling 100 pens, gains the selling price of 20 pens, gain percent
Lead-in keywords: Find
Negative lead-in flag: false

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Practise the full RRB Staff Nurse Jaipur-6th June 2018

Attempt every question from this paper in a timed mock, then review the full solution for each one.