When 2 is subtracted from each of the given n numbers, then the sum of the numbers so obtained is 102. When 5 is subtracted from each of them, then the sum of the numbers so obtained is 12. What is the average of the given n numbers?

5.4

Let sum of n numbers be x, then

x - 2n = 102  ...(1)

x - 5n = 12    ....(2)

Subtract (1) from (2)

3n = 90

n = 30

from eq. (1)

x - 60 = 102

⇒ x = 102 + 60 = 162

Average of first n numbers = \(\frac{162}{30}\) = 5.4