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Profit percentage in sequential transactions

CAT 2023 Slot 2 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 Slot 2 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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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

Explanation

  1. Minu buys at Rs. 1000.
  2. Minu sells to Kanu at a 20% profit: Price = 1000×1.20=12001000 \times 1.20 = 1200.
  3. Kanu sells back to Minu at a 20% loss: Price = 1200×0.80=9601200 \times 0.80 = 960.

Net cost incurred by Minu before selling to Tanu = 1000−1200+960=7601000 - 1200 + 960 = 760.

Let the price at which Minu sells to Tanu be PP.

Total profit made by Minu = P−760=500  ⟹  P=1260P - 760 = 500 \implies P = 1260.

When Minu bought the sunglasses back from Kanu, her cost price was Rs. 960 and she sold it to Tanu for Rs. 1260.

Profit on sale to Tanu =1260−960=300= 1260 - 960 = 300.

Profit percentage =300960×100%=31.25%= \frac{300}{960} \times 100\% = 31.25\%.

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