CAT 2023 Slot 2 QA Question & Solution
Question
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
Options
Solution
Let the total number of employees in the company be $100x$, and the total salary of all the employees be $100y$.
It is given that 20% of the employees work in the manufacturing department, and the total salary received by all the manufacturing employees is one-sixth of the total salary of all the employees in the company.
Thus, the total number of employees in the manufacturing department is $20x$, and the total salary received by them is $\frac{100y}{6}$.
The average salary in the manufacturing department is:
$$
\frac{\frac{100y}{6}}{20x} = \frac{5y}{6x}
$$
Similarly, the total number of employees in the non-manufacturing department is $80x$, and the total salary received by them is $\frac{500y}{6}$.
Hence, the average salary in the non-manufacturing department is:
$$
\frac{\frac{500y}{6}}{80x} = \frac{25y}{24x}
$$
Now, the ratio of average salaries in the manufacturing and non-manufacturing departments is:
$$
\frac{\frac{5y}{6x}}{\frac{25y}{24x}} = \frac{5y \times 24x}{6x \times 25y} = \frac{120}{150} = \frac{4}{5}
$$
Therefore, the ratio of average salaries in the manufacturing and non-manufacturing departments is 4:5.
The correct option is B.