In a factory, the average salary of the employees is ₹ 7000. If the average…
2023
In a factory, the average salary of the employees is ₹ 7000. If the average salary of 12 officers is ₹ 40000 and that of the remaining employees is ₹ 6000, then the number of employees is:
Answer: D. 408 — CONCEPTA weighted average is found from total value divided by total count. When a group has subgroups with different averages, each subgroup total equals its…
- A.
402
- B.
404
- C.
406
- D.
408
Attempted by 1 students.
Show answer & explanation
Correct answer: D
CONCEPT
A weighted average is found from total value divided by total count. When a group has subgroups with different averages, each subgroup total equals its count multiplied by its average.
Equivalently, the subgroup above the overall average supplies exactly the excess needed to raise the subgroup below the overall average.
APPLICATION
Let N be the total number of employees, so the number of non-officers is N − 12.
The total salary from the stated overall average is ₹7000N.
The subgroup salary total is 12 × ₹40000 + (N − 12) × ₹6000.
Equating these totals gives 7000N = 480000 + 6000N − 72000 = 6000N + 408000.
Therefore 1000N = 408000, so N = 408 employees.
CROSS-CHECK
The 12 officers earn ₹33000 each above the overall average, contributing 12 × ₹33000 = ₹396000 of excess. The other 396 employees earn ₹1000 each below it, producing an equal ₹396000 deficit. The weighted average is therefore ₹7000, confirming 408 employees.