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?
Answer & explanation
Correct answer: option 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