Ritik bought an article for ₹474 and sold it to Ritika at a loss of 28%. With this amount, Ritik bought another article and sold it at a gain of 75%. What is Ritik's overall gain percentage?

1. A

   26%

2. B

   23%

3. C

   21%

4. D

   29%

Appeared in: DSSSB 13 August 2024

Explanation

• The problem involves two successive percentage changes: a 28% loss followed by a 75% gain.
• The most efficient way to solve this is using the successive percentage change formula: a + b + (ab/100).
• Loss is represented by a negative sign (-28) and gain by a positive sign (+75).
• Plugging in the values: -28 + 75 + (-28 * 75) / 100 = 47 - 21 = 26%.
• The positive result of 26 indicates an overall gain of 26%. The initial cost price of ₹474 is extra information not needed for the percentage calculation.

Why Other Options Were Wrong

• Option B: This is an incorrect calculation and does not match the result from the successive percentage formula.
• Option C: This value (21) represents only the interaction term (ab/100) in the successive percentage formula, not the final answer. It's a common mistake to stop the calculation prematurely.
• Option D: This is an incorrect calculation and does not match the result from the successive percentage formula.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Percentage Change in Profit and Loss as background academic context rather than a clinical decision trigger.
• This type of question tests quantitative aptitude, a common component of competitive examinations for nursing positions and other government jobs.
• Mastering the successive percentage formula (a + b + ab/100) allows for rapid calculation, saving crucial time during timed exams.
• This skill is useful in personal finance for understanding compound interest or successive discounts on purchases.

How to Approach the Question

• Identify that the question asks for an overall percentage change after two successive transactions (a loss then a gain).
• Recognize that the initial cost price (₹474) is not needed to calculate the final percentage change, only the absolute profit/loss amount.
• Recall the formula for successive percentage change: Net Change = a + b + (ab/100), where 'a' and 'b' are the percentage changes.
• Assign signs to the percentages: loss is negative (-28) and gain is positive (+75).
• Substitute the values into the formula and calculate the result to find the net gain or loss percentage.
• Alternatively, assume an initial cost of 100 and calculate the final selling price after both transactions to find the overall percentage change.

Concept Tested & Keywords

• Concept Tested: Successive Percentage Change in Profit and Loss
• Stem keywords: bought, sold, loss, gain, overall gain percentage
• Lead-in keywords: What is

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QesoX_E54g6w0slA2c9GtR

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