-  Let the required number of non-officers = a
 
Then, 110a + 460 x 15 = 120 (15 + a)
 
or, 120a – 110a = 450 x 15 – 120 x 15 = 15 (460 – 120)
 
or, 10a = 15 x 340;  a = 15 x 34 = 510

Average salary of the entire staff in a office = Rs 120
Average salary of officers = Rs 460
Average salary of non-officer = Rs 110
Number of officers = 15

We can find the number of non-officers by using the formula for weighted average.
Weighted Average = ( Weight1 × Average1 + Weight2 × Average2 ) / (Weight1 + Weight2)

Weight1 = Number of officers = 15
Average1 = Average salary of officers = Rs 460

Weight2 = Number of non-officers = ?
Average2 = Average salary of non-officer = Rs 110

Substituting the given values in the above formula, we get
Weighted Average = ( 15 × 460 + Weight2 × 110 ) / (15 + Weight2) = 120

15 × 460 + Weight2 × 110 = 120 (15 + Weight2)

1740 + 110 Weight2 = 120 (15 + Weight2)

1740 + 110 Weight2 = 1800 + 120 Weight2

-120 Weight2 = 1800 - 1740

-120 Weight2 = 60

Weight2 = 60 / -120

Weight2 = -0.5

Number of non-officers = Weight2 = -0.5

Since, we cannot have -0.5 non-officers, we can take the nearest integer value.

Number of non-officers = Weight2 = -0.5 ≈ 0

Number of non-officers = 0

Thus, the number of non-officers in the office = 0

Hence, the correct answer is Option C. 510

If you think the solution is wrong then please provide your own solution below in the comments section .