Question

In an office , there are officers and workers. The average salary of the officers and workers is rs. 20250. The average salary of officers alone is 50000 and that of workers is 15000. If the number of officers are 30, what are the number of workers in the office?

Answer 1

This is a question in which we can use Weighted Mean formula

Weighted Mean is given by

W = (N₁M₁ + N₂M₂) ÷ (N₁ + N₂)

here N₁ and N₂ are number of officers and no. of workers resp

and M₁ and M₂ are mean salary of officers and mean salary of workers resp

W = 20250

N₁ = 30, N₂ = let this be x

M₁ = 50000, M₂ = 15000

Putting values, we get

20250 = [ (30)(50000) + (x)(15000) ] / (x + 30)

20250(x + 30) = 1500000 + 15000x

2025(x + 30) = 150000 + 1500x

2025x + 60750 = 150000 + 1500x

525x = 89250

x = 170

Therefore, no. of workers is 170.

Answer 2

A sinecure... is an office, carrying a salary or otherwise generating income, that requires or involves little or no responsibility, labour, or active service.