A sells a Laptop to B at a loss of 25% and B sells the laptop to C at a profit of 40%. If C purchased the laptop for ₹4,998, then what was the cost price (in ₹) of the laptop for A₇₂₆₁₃

1. A

   4,658

2. B

   4,673

3. C

   4,760

4. D

   4,699

Appeared in: RRB Nsg. Superintendent-2026 (Shift -1st)

Explanation

• The problem involves two successive percentage changes: a 25% loss followed by a 40% profit.
• Let the original cost price for A be 'x'. A 25% loss means A sells the item for x * (1 - 0.25) = 0.75x.
• The new owner, B, then sells it at a 40% profit. This profit is calculated on B's cost price (0.75x). So, the final price is (0.75x) * (1 + 0.40) = 1.05x.
• This final price is given as ₹4,998. Therefore, we can set up the equation: 1.05x = 4,998.
• Solving for x gives x = 4,998 / 1.05, which equals ₹4,760.

Why Other Options Were Wrong

• Option A: If the initial cost price was ₹4,658, the final price after a 25% loss and 40% profit would be 4,658 * 1.05 ≈ ₹4,891, which is not the given final price of ₹4,998.
• Option B: If the initial cost price was ₹4,673, the final price would be 4,673 * 1.05 ≈ ₹4,907, which does not match the given final price.
• Option D: If the initial cost price was ₹4,699, the final price would be 4,699 * 1.05 ≈ ₹4,934, which is incorrect.

Related Visual

• Visual 1: Flowchart - Illustrates the chain of transactions from A to B to C, showing the percentage loss and profit at each stage and how the price changes, leading to the final cost for C.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Profit and Loss as background academic context rather than a clinical decision trigger.
• This is a general aptitude question that tests mathematical reasoning, a skill assessed in many professional entrance exams, including those for nursing.
• While not directly used in clinical patient care, strong numeracy skills are essential for administrative and management roles within healthcare, such as budgeting, resource allocation, and inventory control.
• What if? - If B had sold the laptop at a 20% profit instead of 40%, the final price would be calculated as 0.75x * 1.20 = 0.9x. In that case, the original cost price would have been x = 4998 / 0.9 = ₹5,553.33.

How to Approach the Question

• Step 1: Identify the problem as a successive percentage change question. Let the initial unknown value (A's cost price) be 'x'.
• Step 2: Convert the percentage loss into a decimal multiplier. A 25% loss is equivalent to multiplying by (1 - 0.25) = 0.75.
• Step 3: Convert the percentage profit into a decimal multiplier. A 40% profit is equivalent to multiplying by (1 + 0.40) = 1.40.
• Step 4: Formulate an equation by applying the multipliers successively to 'x' and equating it to the final given value: x * 0.75 * 1.40 = 4,998.
• Step 5: Simplify the equation (x * 1.05 = 4,998) and solve for 'x' to find the original cost price.
• Step 6: Verify your calculation and match the result with the given options.

Concept Tested & Keywords

• Concept Tested: Successive Profit and Loss
• Stem keywords: sells, loss of 25%, profit of 40%, purchased for ₹4,998, cost price
• Lead-in keywords: what was the cost price
• Negative lead-in flag: false

Question ID

QR2sRczilFkfooytfrv115

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