Averages , Ratio and Proportion Question 5 - CAT 2024
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:
Step-by-Step Explanation
Divide the list of 40 employees into 4 consecutive blocks of 10 employees each: A, B, C, and D. Let Sā, Sįµ¦, Sš, and Sš represent the total bonus sums for these blocks in 2022.
- Set up the baseline average equations:
First 30 employees:
(Sā + Sįµ¦ + Sš)/30 = 40,000 ā¹ Sā + Sįµ¦ + Sš = 1,200,000ā--- (1)
Last 30 employees:
(Sįµ¦ + Sš + Sš)/30 = 60,000 ā¹ Sįµ¦ + Sš + Sš = 1,800,000ā--- (2)
First 10 & Last 10:
(Sā + Sš)/20 = 50,000 ā¹ Sā + Sš = 1,000,000ā--- (3)
- Solve for the block aggregates:
Add equations (1) and (2):
Sā + 2(Sįµ¦ + Sš) + Sš = 3,000,000
Substitute Sā + Sš = 1,000,000:
1,000,000 + 2(Sįµ¦ + Sš) = 3,000,000
ā¹ Sįµ¦ + Sš = 1,000,000
- From equation (1):
Sā = 1,200,000 ā 1,000,000 = 200,000
- From equation (2):
Sš = 1,800,000 ā 1,000,000 = 800,000
- Apply the 2023 bonus updates:
- New Sā (100% increase) = 200,000 Ć 2 = 400,000
- New Sš (200% increase) = 800,000 Ć 3 = 2,400,000
- Sįµ¦ + Sš remains unchanged = 1,000,000
Total 2023 Bonus Pool = 400,000 + 1,000,000 + 2,400,000 = 3,800,000
New Overall Average = 3,800,000/40 = 95,000 rupees
Correct Option: A
š” FundaMakers Tip:
Grouping a large dataset into equal, independent blocks simplifies the problem. Dividing the 40 employees into 4 distinct groups of 10 converts a complex multi-variable word problem into a clean three-equation system, helping you find the individual group totals and the new overall average easily.