A man loses 5% by selling a book for ₹ 1,140. At what price should the book be sold to make a profit of 5%?

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

The initial selling price (SP) is ₹ 1,140 with a 5% loss. This means the SP is 95% of the Cost Price (CP).
To find the CP, we calculate: CP = SP / (1 - Loss Percentage) = 1140 / (1 - 0.05) = 1140 / 0.95 = ₹ 1,200.
The goal is to make a 5% profit on the CP of ₹ 1,200.
The new selling price is calculated as: New SP = CP * (1 + Profit Percentage) = 1200 * (1 + 0.05) = 1200 * 1.05.
Multiplying 1200 by 1.05 gives the final selling price of ₹ 1,260.

Option A: This value is only slightly higher than the initial selling price and does not correctly account for the initial 5% loss and the subsequent 5% profit calculation based on the actual cost price.
Option B: This value is significantly higher and results from a miscalculation, possibly by applying the profit percentage incorrectly or making an error while determining the cost price.
Option D: This value is too high and indicates a calculation error. It might arise from incorrectly adding percentages or miscalculating the base cost price.

Visual 1: Flowchart: Step 1: Calculate Cost Price (Given SP = 1140, Loss = 5%). Formula: CP = SP / (1 - 0.05). Result: CP = ₹1200. Step 2: Calculate New Selling Price (Given CP = 1200, Profit = 5%). Formula: New SP = CP * (1 + 0.05). Result: New SP = ₹1260.

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 question tests basic numeracy and problem-solving skills, which are fundamental for nurses.
Nurses use mathematical calculations daily for tasks such as medication dosage calculation, IV drip rate monitoring, and interpreting patient data, where accuracy is critical for patient safety.
What if the initial sale resulted in a 10% loss? The CP would be 1140 / 0.90 = ₹1266.67. A 5% profit would then require a selling price of 1266.67 * 1.05 = ₹1330.

How to Approach the Question

First, identify the given information: the initial selling price (SP1 = ₹1,140) and the loss percentage (5%).
Recognize that a 5% loss means the book was sold for 95% (100% - 5%) of its cost price (CP).
Set up the equation: 0.95 × CP = ₹1,140.
Solve for the CP: CP = ₹1,140 / 0.95 = ₹1,200.
Now, calculate the new selling price (SP2) needed to make a 5% profit on the CP.
Set up the equation for profit: SP2 = CP × (1 + 5/100) = ₹1,200 × 1.05.

Concept Tested & Keywords

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