CAT 2024 Slot 2 QA Q10 Ratio, Mixtures & Averages

Question 10 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was
  1. A
    90000
  2. B
    95000
  3. C
    80000
  4. D
    85000

Answer: (B) 95000 Ratio, Mixtures & Averages MCQ

Solution

  1. Let the bonus totals of the first 10, middle 20 and last 10 be \(F, M, L\) (in Rs).
  2. \(F+M = 30 \times 40000 = 1{,}200{,}000\), \(M+L = 1{,}800{,}000\), \(F+L = 20 \times 50000 = 1{,}000{,}000\).
  3. Adding: \(F+M+L = 2{,}000{,}000\), so \(F = 200{,}000\), \(M = 1{,}000{,}000\), \(L = 800{,}000\).
  4. In 2023: \(2F + M + 3L = 400{,}000 + 1{,}000{,}000 + 2{,}400{,}000 = 3{,}800{,}000\).
  5. Average \(= \frac{3{,}800{,}000}{40} = 95000\).

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