The sum of nine consecutive natural numbers is 2088 . The average of prime numbers among these numbers is

Correct option is B

Given:
Sum of 9 consecutive natural numbers = 2088
Formula Used:
Average of n consecutive numbers = $$\frac{Sum}{n}.$$​ This average is also the middle term when n is odd.
Solution:
The middle term (5th term) of the 9 consecutive numbers is $$\frac{2088}{9}$$​ = 232.
Since 232 is the 5th term, the sequence of 9 numbers is: 228, 229, 230, 231, 232, 233, 234, 235, 236.
We must find the prime numbers within this set. We eliminate all even numbers: 228, 230, 232, 234, 236.
Check remaining odd numbers: 229, 231, 233, 235.
235 is divisible by 5.
231 is divisible by 3 (sum of digits 2 + 3 + 1 = 6)
229 and 233 have no simple prime factors and are prime numbers.
Average of these prime numbers = $$\frac{229 + 233}{2} = \frac{462}{2} = 231.$$​​
Final Answer
So the correct answer is (b)