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40% of the employees in a factory are wo...

40% of the employees in a factory are workers. All the remaining employees are executives .The annual income of each worder is $390. The annual income of each executive is $420. What is the average annual incomes of all the employees in the factory together?

A

390

B

405

C

408

D

415

Text Solution

AI Generated Solution

The correct Answer is:
To find the average annual income of all the employees in the factory, we can follow these steps: ### Step 1: Define the total number of employees Let the total number of employees in the factory be \( X \). ### Step 2: Calculate the number of workers and executives Since 40% of the employees are workers, the number of workers can be calculated as: \[ \text{Number of workers} = 0.4X \] The remaining employees are executives, which is 60% of the total employees: \[ \text{Number of executives} = 0.6X \] ### Step 3: Calculate the total income of workers The annual income of each worker is $390. Therefore, the total income of all workers is: \[ \text{Total income of workers} = \text{Number of workers} \times \text{Income per worker} = 0.4X \times 390 = 156X \] ### Step 4: Calculate the total income of executives The annual income of each executive is $420. Therefore, the total income of all executives is: \[ \text{Total income of executives} = \text{Number of executives} \times \text{Income per executive} = 0.6X \times 420 = 252X \] ### Step 5: Calculate the total income of all employees Now, we can find the total income of all employees by adding the total income of workers and executives: \[ \text{Total income of all employees} = \text{Total income of workers} + \text{Total income of executives} = 156X + 252X = 408X \] ### Step 6: Calculate the average annual income The average annual income of all employees is given by the total income divided by the total number of employees: \[ \text{Average annual income} = \frac{\text{Total income of all employees}}{\text{Total number of employees}} = \frac{408X}{X} = 408 \] ### Final Answer The average annual income of all the employees in the factory together is **$408**. ---
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