Averages , Ratio and Proportion Question 2 - CAT 2025
The average salary of 5 managers and 25 engineers in a company is 60,000 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 Value Shifts:
Let the average salary of the managers be M and that of the engineers be E.
Total original salary pool = 30 employees × 60,000 = 1,800,000 rupees
The problem states that a 20% increase in each manager's salary raises the company's overall average salary by 5%.
Net increase in salary pool = 5% of 1,800,000 = 90,000 rupees
- Isolate Manager and Engineer Components:
This 90,000 rupee increase is generated entirely by the 20% salary hike distributed across the 5 managers:
5 × (0.20M) = 90,000 ⟹ M = 90,000 rupees
The average manager baseline salary is 90,000 rupees.
Now, substitute M = 90,000 back into the original aggregate formula to solve for E:
5(90,000) + 25E = 1,800,000
450,000 + 25E = 1,800,000
25E = 1,350,000 ⟹ E = 1,350,000/25 = 54,000 rupees
Correct Option: C
💡 FundaMakers Tip:
Use the Incremental Deviation Method. Do not write separate, long simultaneous equations for the before and after states. Isolate the net change (5% of total = 90,000) and map it directly to the component that caused it (20% of 5 managers). This isolates M instantly and simplifies the remaining steps.