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Discount and Profit Calculation

CAT 2025 Slot 1 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2025 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Answer

175

Explanation

Cost price of 1 chair = Rs 100. Total CP for 13 chairs given = 13×100=Rs 130013 \times 100 = \text{Rs } 1300. Overall profit = 26%, so Total Revenue = 1.26×1300=Rs 16381.26 \times 1300 = \text{Rs } 1638. This total revenue is obtained by charging the discounted selling price for 12 chairs: Selling Price per chair SP=163812=136.5\text{Selling Price per chair } SP = \frac{1638}{12} = 136.5 Discount offered = 22%, so SP=0.78×MPSP = 0.78 \times MP: MP=136.50.78=175MP = \frac{136.5}{0.78} = 175 Thus, the marked price of each chair is Rs 175.

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