The average salary per head of all workers in an institution is ₹60. The average salary per head of 12 officers is ₹400, and the average salary per head of the rest is ₹56. What is the total number of workers?

Introduction / Context:This is a weighted-average headcount problem. Knowing subgroup means and the overall mean allows solving for the total size using a single linear equation in N, the total workers.

Given Data / Assumptions:

• Total workers = N (unknown).
• Officers: 12 with mean ₹400.
• Others: N − 12 with mean ₹56.
• Overall mean = ₹60.

Concept / Approach:Set (12 * 400 + (N − 12) * 56) / N = 60 and solve for N. Multiply both sides by N to remove the denominator and simplify.

Step-by-Step Solution:

Verification / Alternative check:Check totals: Officers 12 * 400 = 4800; Others (1032 − 12) * 56 = 1020 * 56 = 57120; Grand total = 61920; Average = 61920 / 1032 = 60. Verified.

Why Other Options Are Wrong:1030, 1060, 1062: Do not satisfy the linear relation required by the overall mean of ₹60.

Common Pitfalls:Using an unweighted mean of 400 and 56 or forgetting to include the officers' count separately from the others.

Final Answer:1032