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 Cost Price (CP) is defined as 7/9 of the article's value (V), so CP = (7/9)V.
The Selling Price (SP) is 20% more than the value, so SP = V + 0.20V = 1.2V or (6/5)V.
The gain is the difference between SP and CP: Gain = (6/5)V - (7/9)V = (19/45)V.
Gain Percentage is calculated as (Gain / CP) × 100.
Substituting the values: [(19V/45) / (7V/9)] × 100 = (19/35) × 100, which is approximately 54.3%.

Option A: This is a miscalculation and does not reflect the correct gain based on the given cost and selling prices.
Option B: This error likely arises from incorrectly using the article's original value (V) as the denominator for the percentage calculation, i.e., (Gain / V) x 100, instead of the Cost Price (CP).
Option C: This error could happen if the 20% increase was mistakenly applied to the cost price (7/9 V) instead of the article's value (V) when calculating the selling price.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of gain percentage in a profit and loss problem as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude, a key component of the general intelligence and reasoning sections of nursing entrance examinations.
While not a direct clinical task, strong numeracy skills are fundamental for nurses in various daily activities, including accurate medication dosage calculation, setting IV drip rates, and interpreting patient data from charts and monitors.
What if the article was sold for 10% less than its value? The SP would be 0.9V. The gain would be (0.9V - 7/9V) = (8.1V - 7V)/9 = 1.1V/9. The gain percentage would then be ((1.1V/9) / (7V/9)) * 100 = (1.1/7) * 100 ≈ 15.7%.

How to Approach the Question

First, carefully read the question to identify the cost price (CP) and selling price (SP) in relation to the article's 'value'.
Let the value of the article be an unknown variable, 'V'. Alternatively, to simplify, assume a value that is a multiple of the denominators (e.g., 9 x 5 = 45, so let V = 45).
Express the CP in terms of V: CP = (7/9)V.
Express the SP in terms of V: SP = V + 20% of V = 1.2V.
Calculate the absolute gain by subtracting the CP from the SP: Gain = SP - CP.
Use the standard formula for gain percentage: Gain % = (Gain / Cost Price) × 100.

Concept Tested & Keywords

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