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

Question: 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is BDT 390. The annual income of each executive is BDT 420. What is the average annual income of all the employees in the factory together?

Solution:
Let,
P be the number of employees.
Now,
40% of P = 0.4P
Hence,
the number of workers is 2P/5

All the remaining employees are executives,
So the number of executives = P - (2P/5) = 3P/5
The total annual income of all workers together = 2P/5 × 390 = 156P
The total income of all the executives together = 3P/5 × 420 = 252P
Hence, the total income of the employees = 156P + 252P = 408P
The average income of all the employees together = 408