Question:

A shopkeeper offers a discount of $22%$ on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of $26%$ on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is:

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When a shopkeeper gives more items than charged (like “13 for the price of 12”), treat all given items as contributing to total cost but only the charged items as contributing to revenue.
Updated On: Dec 5, 2025
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Correct Answer: 175

Solution and Explanation

Let the marked price of one chair be \(M\). Step 1: Compute total cost price. The shopkeeper gives \emph{13 chairs} to the customer but incurs cost on all 13. \[ \text{Total CP} = 13 \times 100 = 1300. \]
Step 2: Compute total selling price using profit. Profit percentage is \(26%\). \[ \text{Total SP} = \text{CP} \times (1 + 0.26) = 1300 \times 1.26 = 1638. \]
Step 3: Write selling price equation using discount and number of chairs charged. The customer pays for *12 chairs*, each at the discounted price. \[ \text{Discounted price per chair} = M(1 - 0.22) = 0.78M. \] Total amount collected: \[ 12 \times 0.78M = 9.36M. \] This must equal the total SP: \[ 9.36M = 1638. \]
Step 4: Solve for \(M\). \[ M = \frac{1638}{9.36} = 175. \] Thus, the marked price per chair is: \[ \boxed{175}. \]
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