CAT 2022 Slot 1 QA Q9 Percentages & Profit-Loss

Question 9 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
  1. A
    1440
  2. B
    1176
  3. C
    1680
  4. D
    2520

Answer: (C) 1680 Percentages & Profit-Loss MCQ

Solution

  1. Let \(7c = 30p = 9a = 630k\) (per-kg prices), so \(c = 90k, p = 21k, a = 70k\).
  2. Total cost \(= 4(90k) + 14(21k) + 6(70k) = 360k + 294k + 420k = 1074k\) for 24 kg.
  3. With marked price \(M\) per kg: \(24M = 1074k + 1752\), and actual revenue \(4M + 20(0.8M) = 20M = 1074k + 744\).
  4. From the first, \(20M = \frac{5}{6}(1074k + 1752) = 895k + 1460\). So \(895k + 1460 = 1074k + 744 \Rightarrow 179k = 716 \Rightarrow k = 4\).
  5. Spent on almonds \(= 420k = 1680\).

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