CAT 2022 Slot 1 QA Q14 Ratio, Mixtures & Averages

Question 14 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is

TITA: type in the answer. There are no options and no negative marking.

Answer: 160 Ratio, Mixtures & Averages TITA

Solution

  1. Let juice cost \(j\) per kg; syrup \(= 0.8j\). Total cost \(= 110(0.8j) + 120j = 208j\).
  2. Target revenue at 64% profit \(= 1.64 \times 208j = 341.12j\).
  3. Revenue from the separate sales: syrup \(10 \times 0.8j \times 1.1 = 8.8j\), juice \(20 \times 1.2j = 24j\), total \(32.8j\).
  4. Remaining 100 kg syrup + 100 kg juice sold at 308.32: \(200 \times 308.32 = 61664 = 341.12j - 32.8j = 308.32j\), so \(j = 200\).
  5. Syrup cost \(= 0.8 \times 200 = 160\) per kg.

Same concept in other years

See every question on Selling parts at different prices, rest as a mixture, to hit an overall profit.

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