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?

1 390
2405
3408
4415

Answer:- 1

Explanation:-

Solution:

\begin{aligned} L e t X b e t h e n u m b e r o f e m p l o y e e s . \\ We are given that 40 % of the employees are workers . \\ Now, 40 % of X is (\frac{40}{100}) \times X = 0.4 X \\ Hence, the number of workers is \frac{2 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 X}{5}) \\ = (\frac{3 X}{5}) \\ The annual income of each worker is R s . 390. \\ Hence, the total annual income of all workers together is \\ = (\frac{2 X}{5}) \times 390 = 156 X \\ Also, the annual income of each executive is R s . 420. \\ Hence, the total income of all the executives together is, \\ (\frac{3 X}{5}) \times 420 = 252 X \\ Hence, the total income of the employees is, \\ = 156 X + 252 X = 408 X \\ The average income of all the employees together equals \end{aligned}

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