Explanation:

Let for 'n' numbers the average be 'x'.
So, the total sum of 'n' numbers would be 'nx'.
If 2 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = 2n
Thus, value of the total sum now = (nx - 2n)
Given that, this value equals to 102.
So, nx - 2n = 102 ...(1)
Again when 5 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = 5n
×
×100 +
120
(300 − x) × 100 =
90
300
? Thus, value of the total sum now = (nx - 5n)
Given that, this value equals to 12.
So, nx - 5n = 12 ...(2)
Subtracting (2) from (1), we get:
nx - 2n - (nx - 5n) = 102 - 12
⇒ -2n + 5n = 90
⇒ 3n = 90
⇒ n = 90/3 = 30
There are 30 numbers.
Putting n = 30, in eqn.(1), we get:
(30)x - 2(30) = 102
⇒ 30x - 60 = 102
⇒ 30x = 162
⇒ x = 162/30 = 5.4
The average of 30 numbers is 5.4.