Averages , Ratio and Proportion Question 3 - CAT 2023
In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is:
Step-by-Step Explanation
Assume convenient numbers for the percentages and fractions.
Let the Total Number of Employees be 100.
Let the Total Salary of the Company be 600 units (choosing a multiple of 6 to make the 1/6 fraction clean).
- Analyze the Manufacturing (Mfg) Department:
Employees = 20% of 100 = 20
Total Salary = 1/6 of 600 = 100 units
Average Salaryₘfg = 100/20 = 5 units/employee
- Analyze the Non-Manufacturing (Non-Mfg) Department:
Employees = 100 − 20 = 80
Total Salary = 600 − 100 = 500 units
Average Salaryₙₒₙ₋Mfg = 500/80 = 50/8 = 25/4 units/employee
- Calculate the Ratio:
Ratio = Average Salaryₘfg/Average Salaryₙₒₙ₋Mfg
= 5/(25/4) = 5 × 4/25 = 20/25 = 4/5
Ratio = 4 : 5
Correct Option: B
💡 FundaMakers Tip:
Never use x and y for ratio-based average problems! Pick a "Smart Base" that perfectly accommodates all the fractions and percentages given in the problem. 100 employees and 600 salary units ensure you deal entirely with clean integers until the final ratio.