CAT 2022 Slot 1 QA Q8 Ratio, Mixtures & Averages

Question 8 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

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

Answer: 111 Ratio, Mixtures & Averages TITA

Solution

  1. Let ahead \(= 3k\), behind \(= 5k\). Total including Pinky \(= 8k + 1 \lt 300\).
  2. \(8k \le 298 \Rightarrow k \le 37\).
  3. Maximum persons ahead \(= 3 \times 37 = 111\).

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