Average, Mixture and Alligation Question 3 - CAT 2025
The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received a 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is:
Step-by-Step Explanation
- Analyze the total salary delta:
Total number of employees = 5 + 25 = 30.
The initial overall average salary is 60000 rupees.
When managers get a 20% hike, the global average increases by 5%.
Total increase in company expenditure = 30 × 5% of 60000 = 30 × 3000 = 90000 rupees
- Isolate Manager and Engineer Salaries:
Since the engineers' salaries remained unchanged, this entire 90000 rupee increase comes strictly from the 20% raise given to the 5 managers.
20% of Total Initial Manager Salary = 90000
Total Initial Manager Salary = 90000 × 5 = 450000 rupees
Now, calculate the total initial pool for the entire company:
Total Initial Salary = 30 × 60000 = 1800000 rupees
Total Initial Engineer Salary = 1800000 − 450000 = 1350000 rupees
Average Salary of Engineers = 1350000 / 25 = 54000 rupees
Correct Option: C
💡 FundaMakers Tip:
Use the Deviation Method to bypass simultaneous linear equations. Recognize that an overall increase of 5% across 30 parts requires a total of 150 percentage-units of growth. Since this growth is supplied entirely by 5 managers expanding at 20% each (5 × 20 = 100 percentage-units), the base values must balance out linearly, saving you multiple algebraic steps.