CAT 2023 Slot 3 QA Q12 Ratio, Mixtures & Averages

Question 12 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

There are three persons \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) in a room. If a person \(\mathrm{D}\) joins the room, the average weight of the persons in the room reduces by \(x \mathrm{~kg}\). Instead of \(\mathrm{D}\), if person \(\mathrm{E}\) joins the room, the average weight of the persons in the room increases by \(2 x \mathrm{~kg}\). If the weight of \(\mathrm{E}\) is \(12 \mathrm{~kg}\) more than that of \(\mathrm{D}\), then the value of \(x\) is
  1. A
    1.5
  2. B
    2
  3. C
    0.5
  4. D
    1

Answer: (D) 1 Ratio, Mixtures & Averages MCQ

Solution

  1. Let the average of A, B, C be \(a\) (total \(3a\)).
  2. With D: \(\frac{3a+D}{4} = a-x \Rightarrow D = a-4x\). With E: \(\frac{3a+E}{4}=a+2x \Rightarrow E = a+8x\).
  3. \(E-D = 12x = 12 \Rightarrow x=1\).

Same concept in other years

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