A shopkeeper professes to sell his goods at a 75% loss but uses a false balance and gains 90%. The actual weight (correct to one decimal place) he uses for 1 kg is:

1. A

   136.6 gm

2. B

   133.8 gm

3. C

   134.2 gm

4. D

   131.6 gm

Appeared in: DSSSB 12 August 2024

Explanation

• The core of this problem is to find a single selling price value from two different perspectives: the shopkeeper's claim and the shopkeeper's actual gain.
• First, calculate the selling price based on the claim. If the cost of 1000 gm is assumed to be ₹1000, a 75% loss means the selling price is ₹1000 * (1 - 0.75) = ₹250.
• Next, model the actual transaction. The shopkeeper sells an unknown weight 'x' (with a cost of ₹x) and makes a 90% profit. So, the selling price is also expressed as x * (1 + 0.90) = 1.9x.
• By equating the two expressions for the selling price (250 = 1.9x), we can solve for the unknown weight 'x'.
• Solving for x gives 250 / 1.9, which is approximately 131.58 gm. Rounding to one decimal place gives 131.6 gm.

Why Other Options Were Wrong

• Option A: If the shopkeeper uses 136.6 gm (actual cost ₹136.6) and sells it for ₹250, the profit is ₹113.4. The profit percentage would be (113.4 / 136.6) * 100 ≈ 83%, which is not the 90% gain stated in the problem.
• Option B: If the shopkeeper uses 133.8 gm (actual cost ₹133.8) and sells it for ₹250, the profit is ₹116.2. The profit percentage would be (116.2 / 133.8) * 100 ≈ 86.8%, which is not the 90% gain stated in the problem.
• Option C: If the shopkeeper uses 134.2 gm (actual cost ₹134.2) and sells it for ₹250, the profit is ₹115.8. The profit percentage would be (115.8 / 134.2) * 100 ≈ 86.3%, which is not the 90% gain stated in the problem.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss with Faulty Weights as background academic context rather than a clinical decision trigger.
• This type of problem tests logical reasoning and the ability to work with percentages, which is a fundamental skill in quantitative aptitude sections of competitive exams.
• The key takeaway is to distinguish between the 'professed' or 'face value' of a transaction and the 'actual' transaction, a common theme in faulty weight problems.
• What if the shopkeeper professed a 75% loss but actually incurred a 10% loss? In that case, the equation would be 250 = x * (1 - 0.10) = 0.9x. The actual weight used would be x = 250 / 0.9 ≈ 277.8 gm, which is more than the correct answer, as the profit margin is much lower.

How to Approach the Question

• First, standardize the cost. Assume the cost price of 1 gram is a simple unit, like ₹1. This makes the cost of 1 kg (1000 gm) equal to ₹1000.
• Second, calculate the professed selling price. Based on the shopkeeper's claim (75% loss), determine the price the customer pays for the item.
• Third, define the unknown. Let 'x' be the actual weight in grams that the shopkeeper is using. The actual cost to the shopkeeper is therefore ₹x.
• Fourth, formulate the actual profit equation. The selling price (calculated in step 2) must equal the actual cost (₹x) plus the actual profit (90% of ₹x).
• Finally, set the two expressions for the selling price equal to each other and solve the resulting equation for 'x' to find the actual weight used.

Concept Tested & Keywords

• Concept Tested: Profit and Loss with Faulty Weights
• Stem keywords: shopkeeper, professes, loss, false balance, gains, actual weight, 1 kg
• Lead-in keywords: The actual weight is
• Negative lead-in flag: false

Question ID

QEff0_Skt6QkqPCzQb2vGG

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