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
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
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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.
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.
Updated On: Dec 5, 2025
- \(40000\)
- \(54000\)
- \(50000\)
- \(45000\)
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The Correct Option is B
Solution and Explanation
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: \[ \boxed{54000}. \]
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: \[ \boxed{54000}. \]
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