Question

In a company there are 252 engineers, in which the ratio of the number of electronics engineers and computer engineers is 2: 1. The ratio of the number of electronics engineers and computer engineers becomes 1 : 1 after recruitment of some more computer engineers. The average age of all the engineers is now 22 years and the average age of the computer engineers is 2 years less than the average age of electronics engineers.
(A) The average age (in years) of electronics engineers is 21
(B) The average age (in years) of computer engineers is 21 
(C) The average age (in years) of electronics engineers is 23 
(D) The average age (in years) of electronics engineers is 25  
(E) The average age (in years) of computer engineers is 23 Choose the correct answer from the options given below:

• (A) and (E) only
• (B) and (C) only
• (D) and (E) only
• (E) only

Answer 1

The Correct Option is B

In this problem, we need to determine the average ages of electronics engineers and computer engineers based on the given conditions and select the correct options.

1. Initially, the ratio of electronics engineers to computer engineers is \(2:1\). Let the number of electronics engineers be \(2x\) and the number of computer engineers be \(x\).
2. The total number of engineers is \(252\), so: \(2x + x = 252\)  
   Simplifying this equation gives: \(3x = 252 \Rightarrow x = 84\)
3. Thus, the number of electronics engineers is \(2x = 168\) and the number of computer engineers is \(x = 84\).
4. After recruiting more computer engineers, the ratio becomes \(1:1\). Therefore, the new number of computer engineers is \(168\).
5. The number of additional computer engineers recruited is: \(168 - 84 = 84\).
6. The average age of all engineers is given as \(22\) years. Let the average age of electronics engineers be \(E\) years and that of computer engineers be \(C\) years. From the problem, \(C = E - 2\).
7. According to the average calculation: \(\frac{168E + 168(E - 2)}{336} = 22\)
8. Simplifying the equation: \(\frac{168E + 168E - 336}{336} = 22\)
9. This further simplifies to: \(336E - 336 = 7392 \Rightarrow 336E = 7728 \Rightarrow E = \frac{7728}{336} = 23\)
10. Thus, the average age of electronics engineers is \(23\) years.
11. Using \(C = E - 2\), the average age of computer engineers is: \(C = 23 - 2 = 21\) years.

Based on the calculations above, the correct options are (B) and (C) only: The average age of electronics engineers is 23, and the average age of computer engineers is 21.