CAT 2023 Slot 3 QA Q11 Percentages & Profit-Loss

Question 11 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
  1. A
    4.2%
  2. B
    15.5%
  3. C
    16%
  4. D
    9.7%

Answer: (B) 15.5% Percentages & Profit-Loss MCQ

Solution

  1. Cost: Rs 100 buys 105 cm, so 95 cm costs \(\frac{95\times100}{105} \approx 90.48\).
  2. Sale: a customer pays for 1 m at Rs 110 less 5%, i.e. Rs 104.5, but receives only 95 cm.
  3. Profit \(= \frac{104.5\times105}{9500} - 1 = \frac{109.725}{95}-1 = 0.155 = 15.5\%\).

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