The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is -

A. 20

B. 30

C. 15

D. 10

Answer: Option D

Solution(By Examveda Team)

Let the number of natural numbers = n
∵ The average of some natural numbers = 15
⇒ Sum of these natural number = 15 × n = 15n
∵ 30 is added and 5 is subtracted
So, now addition of these number
= 15n + 30 - 5
= 15n + 25
According to the question,
⇒ $$\frac{15n + 25}{n}$$ = 17.5
⇒ 15n + 25 = 17.5n
⇒ 2.5n = 25
⇒ n = 10
Therefore, the numbers of natural numbers n = 10