Averages and Percentage Increases in Employee Bonus

CAT 2024 Slot 2 · QA · Medium · Arithmetic

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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

Explanation

Let S1,S2,S3S_1, S_2, S_3 be the sum of bonuses of the first 10, middle 20, and last 10 employees in 2022 respectively.

From given data for 2022:

  1. S1+S2=30×40000=1,200,000S_1 + S_2 = 30 \times 40000 = 1,200,000
  2. S2+S3=30×60000=1,800,000S_2 + S_3 = 30 \times 60000 = 1,800,000
  3. S1+S3=20×50000=1,000,000S_1 + S_3 = 20 \times 50000 = 1,000,000

Summing all three equations: 2(S1+S2+S3)=4,000,000  ⟹  S1+S2+S3=2,000,0002(S_1 + S_2 + S_3) = 4,000,000 \implies S_1 + S_2 + S_3 = 2,000,000

Subtracting individual equations gives:

  • S1=2,000,000−1,800,000=200,000S_1 = 2,000,000 - 1,800,000 = 200,000
  • S3=2,000,000−1,200,000=800,000S_3 = 2,000,000 - 1,200,000 = 800,000
  • S2=1,000,000S_2 = 1,000,000

In 2023:

  • Sum of first 10 increases by 100%: S1′=2S1=400,000S_1' = 2 S_1 = 400,000
  • Sum of last 10 increases by 200%: S3′=3S3=2,400,000S_3' = 3 S_3 = 2,400,000
  • Sum of middle 20 remains unchanged: S2′=S2=1,000,000S_2' = S_2 = 1,000,000

Total bonus in 2023 = 400,000+1,000,000+2,400,000=3,800,000400,000 + 1,000,000 + 2,400,000 = 3,800,000. Average bonus of all 40 employees = 3,800,00040=95000\frac{3,800,000}{40} = 95000.

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