Question:

Tarun got 30% concession on the labelled price of an article and sold it for Rs.8,750 with 25% profit on the price he bought. What was the labelled price?

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You can work backwards: If SP is \(8750\) with a \(25%\) profit (\(5/4\) of CP), then \(\text{CP} = 8750 \times (4/5) = 7000\). If CP is \(7000\) after a \(30%\) discount (\(70%\) of Labelled Price), then \(\text{Labelled Price} = 7000 / 0.7 = 10000\).
Updated On: May 9, 2026
  • Rs.10,000
  • Rs.12,000
  • Rs.16,000
  • Rs.18,000
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The Correct Option is A

Solution and Explanation



Step 1: Understanding the Question:

We need to find the original labelled price of an article. We know the discount percentage Tarun received, his profit percentage when he sold it, and his final selling price.


Step 2: Key Formula or Approach:

Let the Labelled Price be \(L\).
\(\text{Cost Price (CP)} = L \times \left(1 - \frac{\text{Discount %}}{100}\right)\).
\(\text{Selling Price (SP)} = \text{CP} \times \left(1 + \frac{\text{Profit %}}{100}\right)\).


Step 3: Detailed Explanation:

Let the labelled price of the article be \(x\).
Tarun bought it at a \(30%\) concession (discount).
So, his Cost Price (CP) is \(x - 0.30x = 0.70x\).
He sold the article for Rs. \(8,750\) and made a \(25%\) profit on his cost price.
Therefore, the Selling Price (SP) is: \[ \text{SP} = \text{CP} \times 1.25 \] \[ 8750 = 0.70x \times 1.25 \] \[ 8750 = 0.875x \] Now, solve for \(x\): \[ x = \frac{8750}{0.875} \] To simplify, multiply the numerator and denominator by \(1000\): \[ x = \frac{8750000}{875} = 10000 \] The labelled price was Rs. \(10,000\).


Step 4: Final Answer:

The labelled price was Rs. \(10,000\).
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