CAT 2024 Slot 1 QA Q21 Percentages & Profit-Loss

Question 21 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
  1. A
    10
  2. B
    15
  3. C
    20
  4. D
    14

Answer: (D) 14 Percentages & Profit-Loss MCQ

Solution

  1. Let cost price \(= c\); selling price \(= 1.4c\).
  2. New cost \(= 0.6c\), new selling price \(= 1.4c - 5\), with 50% profit: \(1.4c - 5 = 1.5 \times 0.6c = 0.9c\).
  3. \(0.5c = 5 \Rightarrow c = 10\); original selling price \(= 14\).

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