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CAT 2023 Slot 2 QA Question 10

Multiple choice (+3 / −1) · Arithmetic · Ratio, Proportion & Variation · Try it, then check the answer and solution below.

CAT 2023 Slot 2QAArithmetic • Ratio, Proportion & VariationEasy
In a company, 20%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 non-manufacturing employees is
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Answer and solution

Answer: B) 4:54:5

📌 Core Concept
The problem involves ratios and proportions, specifically comparing average salaries between two groups. The key formula used is:
Average Salary=Total SalaryNumber of Employees\text{Average Salary} = \frac{\text{Total Salary}}{\text{Number of Employees}}
🔢 Step-by-Step Solution
1
Define Variables:
Let total number of employees = N$
Total salary of the company = S$
Manufacturing employees = 0.2N$
Non-manufacturing employees = 0.8N$
Total salary for manufacturing = S6\frac{S}{6}$
Total salary for non-manufacturing = 5S6\frac{5S}{6}$
2
Calculate Average Salaries:
Average salary (manufacturing) = S/60.2N\frac{S/6}{0.2N} = S6×0.2N\frac{S}{6 × 0.2N} = S1.2N\frac{S}{1.2N}$
Average salary (non-manufacturing) = 5S/60.8N\frac{5S/6}{0.8N} = 5S6×0.8N\frac{5S}{6 × 0.8N} = 5S4.8N\frac{5S}{4.8N}$
3
Compute the Ratio:
Ratio=S1.2N5S4.8N=S1.2N×4.8N5S=4.81.2×5=4.86=45\text{Ratio} = \frac{\frac{S}{1.2N}}{\frac{5S}{4.8N}} = \frac{S}{1.2N} \times \frac{4.8N}{5S} = \frac{4.8}{1.2 \times 5} = \frac{4.8}{6} = \frac{4}{5}
⚡ 30-Second Shortcut
Recognize that the ratio of averages can be directly computed using the formula:
Ratio=Total Salary (Manufacturing)Total Salary (Non-Manufacturing)×Non-Manufacturing EmployeesManufacturing Employees\text{Ratio} = \frac{\text{Total Salary (Manufacturing)}}{\text{Total Salary (Non-Manufacturing)}} \times \frac{\text{Non-Manufacturing Employees}}{\text{Manufacturing Employees}}
Plugging in the values: $$ \text{Ratio} = \frac{1/6}{

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