Question

In a certain manufacturing plant, the ratio of the number of workers to managers is 7: 2. The total number of employees which consists of workers and managers only is 45,000. The manufacturing plant plans to hire new employees such that for every five workers there is a manager. How many new workers should the manufacturing plant hire?

• A. 26,000
• B. 20,000
• C. 15,000
• D. 10,000

Answer 1

The Correct Option is C

Step 1: Determine the Number of Workers and Managers 

Let the number of workers be 7x and the number of managers be 2x. The total number of employees is:

\[ 7x + 2x = 45,000 \]

Solving for x:

\[ 9x = 45,000 \Rightarrow x = 5,000 \]

Thus, the number of workers is:

\[ 7x = 35,000 \]

And the number of managers is:

\[ 2x = 10,000 \]

Step 2: Adjust for the Desired Worker-to-Manager Ratio

To achieve a ratio of 5 workers to 1 manager, the number of workers should be:

\[ 5 \times 10,000 = 50,000 \]

Thus, the manufacturing plant needs to hire:

\[ 50,000 - 35,000 = 15,000 \]

Final Conclusion:

The number of new workers to be hired is 15,000.

Correct answer: (C) 15,000.