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: Set up two clean equations using the managers' total and the engineers' total as single unknowns (treat each group as one block), then eliminate.

Step 1: Let the managers' total original salary be $M$ and the engineers' total salary be $E$. The combined average of all 30 is 60000, so $$M + E = 30 \times 60000 = 1800000.$$

Step 2: Each manager gets a 20% raise, so the managers' block becomes $1.2M$, while $E$ is unchanged. The new average is 5% higher, giving a new total of $1800000 \times 1.05 = 1890000$. Hence $$1.2M + E = 1890000.$$

Step 3: Subtract the first equation from the second to knock out $E$: \[ (1.2M + E) - (M + E) = 1890000 - 1800000 \] \[ 0.2M = 90000 \implies M = 450000. \]

Step 4: Then $E = 1800000 - 450000 = 1350000$, and the engineers' average is $$\frac{E}{25} = \frac{1350000}{25} = 54000.$$

Final answer: 54000 rupees.