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

Solution(By Examveda Team)

Let X be the number of employees.
We are given that 40% of the employees are workers.
Now, 40% of X is $$\frac{{40}}{{100}}$$ × X = 0.4X
Hence, the number of workers is $$\frac{{2{\text{X}}}}{5}$$
All the remaining employees are executives,
so the number of executives equals,
(The number of Employees) $$ - $$ (The number of Workers)
= X $$ - $$ $$\frac{{2{\text{X}}}}{5}$$
= $$\frac{{3{\text{X}}}}{5}$$
The annual income of each worker is Rs. 390.
Hence, the total annual income of all workers together is
= $$\frac{{2{\text{X}}}}{5}$$ × 390 = 156X
Also, the annual income of each executive is Rs.420.
Hence, the total income {of all the executives together is,
= $$\frac{{3{\text{X}}}}{5}$$ × 420 = 252X
Hence, the total income of the employees is,
= 156X + 252X = 408X
The average income of all the employees together = 408