CAT 2023 Slot 2 QA Q9 Percentages & Profit-Loss

Question 9 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
  1. A
    35.42%
  2. B
    31.25%
  3. C
    52%
  4. D
    26%

Answer: (B) 31.25% Percentages & Profit-Loss MCQ

Solution

  1. Minu buys at 1000 and sells to Kanu at 1200 (profit 200).
  2. Kanu sells it back at 20% loss: \(0.8 \times 1200 = 960\), so Minu's new cost is 960.
  3. Total profit \(200 + (S - 960) = 500\) gives \(S = 1260\).
  4. Profit % on the last sale \(= \frac{1260 - 960}{960}\times 100 = \frac{300}{960}\times100 = 31.25\%\).

Same concept in other years

See every question on Successive resales: multiply the profit and loss factors along the chain.

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