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CAT 2025Slot 1QAQues & Sol

Modern MathHard

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

Solution

1. Concept Used

  • Topic: Profit, Loss, and Discount — Successive Application of Discount and Bonus Quantity
  • Formula: $$\text{Marked Price} = \frac{\text{Discounted Selling Price per chair}}{1 - \text{Discount Rate}}$$

2. Calculation

The cost price of each chair is given as Rs 100. Since the shopkeeper gives 13 chairs but charges the price of only 12 chairs, the total cost incurred by the shopkeeper for 13 chairs is:

$$\text{Total Cost} = 13 \times 100 = \text{Rs } 1300$$

The shopkeeper earns a profit of 26% on this transaction, so the total revenue collected must be:

$$\text{Total Revenue} = 1300 \times 1.26 = \text{Rs } 1638$$

This total revenue of Rs 1638 is collected as the discounted price of 12 chairs (since 13 chairs are given but only 12 are charged for). Therefore, the discounted selling price per chair is:

$$\text{SP}_{\text{disc}} = \frac{1638}{12} = \text{Rs } 136.5$$

Now, since a discount of 22% is applied on the marked price, the discounted price represents 78% of the marked price:

$$\text{SP}_{\text{disc}} = \text{MP} \times (1 - 0.22) = \text{MP} \times 0.78$$

Solving for the Marked Price:

$$\text{MP} = \frac{136.5}{0.78} = \frac{13650}{78} = \text{Rs } 175$$

3. Solution

Answer = 175 ✅

The final calculated Marked Price of each chair is Rs 175.