A person buys an article at 7/9 of its value and sells it for 20 percent more than its value. What is his gain percentage?

Appeared in: KPSC Staff Nurse - 2018

Explanation

The problem requires calculating the gain percentage, which is based on the cost price and the selling price.
The cost price (CP) is 7/9 of the original value, and the selling price (SP) is 120% (or 1.2 times) the original value.
The gain is the difference between SP and CP. The gain percentage is calculated as (Gain / CP) × 100.
Let the value be V. CP = (7/9)V and SP = 1.2V. Gain = (1.2 - 7/9)V = (19/45)V.
Gain % = [(19/45)V / (7/9)V] × 100 = (19/45) × (9/7) × 100 = (19/35) × 100 ≈ 54.3%.

Option A: A 50% gain would occur if the gain was exactly half of the cost price. In this case, a gain of ₹35 on a cost price of ₹70 would be 50%. However, the calculated gain is ₹38.
Option B: This value is a result of miscalculation and does not correspond to the correct application of the profit percentage formula.
Option C: This incorrect value might arise if the gain percentage is wrongly calculated using the original value as the denominator instead of the cost price. For example, (Gain / Original Value) x 100 = (38/90) x 100 = 42.2%, which is also incorrect but illustrates a common mistake.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss Percentage Calculation as background academic context rather than a clinical decision trigger.
This type of problem tests fundamental quantitative reasoning and the ability to break down a multi-step problem into smaller, manageable parts.
Understanding percentages, fractions, and their application is a crucial skill for data interpretation in various fields.
A common error is calculating the percentage based on the original value or selling price instead of the cost price. Always remember that profit/loss percentage is calculated on the cost price unless specified otherwise.

How to Approach the Question

First, identify the key information provided: the relationship between the cost price (CP) and the original value, and the relationship between the selling price (SP) and the original value.
To simplify calculations involving fractions and percentages, assume a convenient number for the original value. Since the fraction is 7/9, a multiple of 9 (like 90 or 900) is an excellent choice.
Calculate the absolute Cost Price (CP) and Selling Price (SP) based on your assumed value.
Determine the absolute gain by subtracting the CP from the SP (Gain = SP - CP).
Apply the standard formula for gain percentage: Gain % = (Gain / CP) × 100. It is critical to use the Cost Price as the denominator.
Perform the final calculation and compare your result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Profit and Loss Percentage Calculation
Stem keywords: buys an article, 7/9 of its value, sells it for 20 percent more, gain percentage
Lead-in keywords: What is

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