Question

The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

• A. \(40000\)
• B. \(54000\)
• C. \(50000\)
• D. \(45000\)

Hint:

In weighted average problems with percentage changes:
Set up equations using total sums (average $\times$ number of people).
Apply the percentage increase only to the relevant group.
Use the new average to form a second equation and solve the system.

Answer 1

The Correct Option is B

Approach: Don't chase the individual salaries. The 5% rise in the overall average comes ENTIRELY from the managers' 20% hike, so the rupee jump in the total bill equals 20% of the managers' total salary. Find that, subtract, and the engineers' total falls out.

Step 1: Total salary of all 30 employees \( = 30 \times 60000 = 1800000 \) rupees.

Step 2: The new average is 5% higher, so the new total salary \( = 1800000 \times 1.05 = 1890000 \) rupees. The increase in the total bill is \[ 1890000 - 1800000 = 90000 \text{ rupees}. \]

Step 3: Only the managers' salaries changed, by 20%. So this 90000 increase is exactly 20% of the managers' original total salary \(M\): \[ 0.20 \, M = 90000 \implies M = 450000 \text{ rupees}. \]

Step 4: Engineers' total salary \( = 1800000 - 450000 = 1350000 \) rupees, shared by 25 engineers: \[ \text{Average} = \frac{1350000}{25} = 54000 \text{ rupees}. \]

Final answer: \(\boxed{54000}\) rupees (option 2).

Why this works: Whenever only one group's value changes, the change in the grand total is fully attributable to that group — so the new average is just a tool to read off that group's contribution.

Answer 2

Let the average salary of each manager be \(M\), and that of each engineer be \(E\).
Step 1: Use the initial average. There are 5 managers and 25 engineers, total 30 employees. \[ \frac{5M + 25E}{30} = 60000 \quad \Rightarrow \quad 5M + 25E = 60000 \times 30 = 1800000. \tag{1} \]
Step 2: Use the new average after managers get 20% hike. Each manager’s new salary: \[ 1.2M. \] Engineers’ salary remains \(E\). New overall average increases by 5%: \[ 60000 \times 1.05 = 63000. \] So, \[ \frac{5(1.2M) + 25E}{30} = 63000 \quad \Rightarrow \quad 6M + 25E = 63000 \times 30 = 1890000. \tag{2} \]
Step 3: Solve the system for \(M\) and \(E\). Subtract (1) from (2): \[ (6M + 25E) - (5M + 25E) = 1890000 - 1800000 \] \[ M = 90000. \] Substitute \(M = 90000\) into (1): \[ 5(90000) + 25E = 1800000 \Rightarrow 450000 + 25E = 1800000 \Rightarrow 25E = 1350000 \Rightarrow E = 54000. \] Thus, the average salary of the engineers is: \[ \boxed{54000}. \]