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CAT 2024 Slot 2 — QA Question 16

Change in AverageEasy

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

Answer & solution

  • 95000

  • B

    85000

  • C

    80000

  • D

    90000

Solution

Hard

Label the four blocks: first 10 (G1G_1), middle 20 (G2G_2, employees 11-30), last 10 (G4G_4, employees 31-40). Convert each average to a total, solve the overlapping sums, then apply the 2023 increases block-by-block.

1

Write the 2022 totals. Let G1,G2,G4G_1,G_2,G_4 be the bonus sums of employees 1-10, 11-30, 31-40.

First 30:G1+G2=30×40000=1,200,000Last 30:G2+G4=30×60000=1,800,000First 10 & last 10:G1+G4=20×50000=1,000,000\begin{aligned} &\text{First 30}: G_1+G_2=30\times 40000=1{,}200{,}000\\ &\text{Last 30}: G_2+G_4=30\times 60000=1{,}800{,}000\\ &\text{First 10 \& last 10}: G_1+G_4=20\times 50000=1{,}000{,}000 \end{aligned}
2

Solve the system. Add the first two and subtract the third.

(G1+G2)+(G2+G4)=3,000,000⇒ (G1+G4)+2G2=3,000,000(regroup)⇒ 1,000,000+2G2=3,000,000 ⇒ G2=1,000,000⇒ G1=1,200,000−G2=200,000,G4=1,000,000−G1=800,000\begin{aligned} &(G_1+G_2)+(G_2+G_4)=3{,}000{,}000\\ &\Rightarrow\ (G_1+G_4)+2G_2=3{,}000{,}000 \quad\text{(regroup)}\\ &\Rightarrow\ 1{,}000{,}000+2G_2=3{,}000{,}000\ \Rightarrow\ G_2=1{,}000{,}000\\ &\Rightarrow\ G_1=1{,}200{,}000-G_2=200{,}000,\quad G_4=1{,}000{,}000-G_1=800{,}000 \end{aligned}
3

Apply 2023 changes. First 10 up 100% (×2\times2), last 10 up 200% (×3\times3), middle 20 unchanged.

2023 total=2G1+G2+3G4⇒ =2(200,000)+1,000,000+3(800,000)⇒ =400,000+1,000,000+2,400,000=3,800,000\begin{aligned} &\text{2023 total}=2G_1+G_2+3G_4\\ &\Rightarrow\ =2(200{,}000)+1{,}000{,}000+3(800{,}000)\\ &\Rightarrow\ =400{,}000+1{,}000{,}000+2{,}400{,}000=3{,}800{,}000 \end{aligned}
4

Average over all 40.

Average=3,800,00040=95,000\begin{aligned} &\text{Average}=\frac{3{,}800{,}000}{40}=95{,}000 \end{aligned}
Average bonus in 2023=Rs 95000\text{Average bonus in 2023}=\text{Rs }95000
CAT 2024 Slot 2 QA Q16: A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of t — Solution | TheCATExam