Study the following information carefully and answer the questions given below:

Eleven persons K, L, M, N, O, P, Q, R, S, T and U were born on the same day of the same month, (but not necessarily in the same order). All of them were born in different years—1981, 1983, 1987, 1994, 1997, 1999, 2000, 2003, 2006, 2007 and 2011 (but not necessarily in the same order). Their ages are to be calculated by considering the base year as 2023.

Age of L is a prime number. The age difference between L and Q is of 3 years. P is three persons younger than Q. O is either five persons elder than L or five persons younger than L. The number of persons elder to O is one less than the number of persons younger to N. T is immediately younger to N. The age difference between R and T is 13 years. R is not immediately elder to Q. Age of M is completely divisible by 4 and is elder to K. S is 2 years elder to K.

If all the persons are arranged in alphabetical order from younger to older than position of how many persons remain unchanged?

First, let us determine the age of each person by using the base year 2023. The ages corresponding to each birth year are:

• 1981: 2023 - 1981 = 42 years
• 1983: 2023 - 1983 = 40 years
• 1987: 2023 - 1987 = 36 years
• 1994: 2023 - 1994 = 29 years
• 1997: 2023 - 1997 = 26 years
• 1999: 2023 - 1999 = 24 years
• 2000: 2023 - 2000 = 23 years
• 2003: 2023 - 2003 = 20 years
• 2006: 2023 - 2006 = 17 years
• 2007: 2023 - 2007 = 16 years
• 2011: 2023 - 2011 = 12 years

Sorting the ages from youngest to oldest gives us the following 11 positions:

Now we analyze the given clues step-by-step to find the correct configuration:

1. Age of L is a prime number: The prime ages in our list are 17, 23, and 29. So, L is either 17, 23, or 29.
2. The age difference between L and Q is 3 years:
   - If L = 17, then Q = 20.
   - If L = 23, then Q = 20 or 26.
   - If L = 29, then Q = 26.
3. P is three persons younger than Q: This means $\mathrm{Position}\left(P\right)=\mathrm{Position}\left(Q\right)-3$.
   - If Q = 20 (Position 4), then P's position is $4-3=1$ (Age 12).
   - If Q = 26 (Position 7), then P's position is $7-3=4$ (Age 20).
4. O is either five persons elder or five persons younger than L:
   - If L = 23 (Position 5) and Q = 20 (Position 4), O's position must be $5+5=10$ (Age 40).
5. The number of persons elder to O is one less than the number of persons younger to N:
   - O is at Position 10, so 1 person is elder to O (at Position 11).
   - Since the number of persons younger to N is 1 more than this, there must be 2 persons younger to N. Thus, N must be at Position 3 (Age 17).
6. T is immediately younger to N: Since N is at Position 3, T must be at Position 2 (Age 16).
7. The age difference between R and T is 13 years: Since T is 16, R's age is $16+13=29$ (Position 8).
8. S is 2 years elder to K: The only remaining consecutive ages with a difference of 2 years are 24 and 26. Thus, K is 24 (Position 6) and S is 26 (Position 7).
9. Age of M is completely divisible by 4 and M is elder to K: The remaining positions are 9 (Age 36) and 11 (Age 42). Since 36 is divisible by 4, M is at Position 9. This leaves U at Position 11 (Age 42).

Therefore, the final arrangement from younger to older is:

Now, let's arrange all 11 persons in alphabetical order from Position 1 (youngest) to Position 11 (oldest) and compare their positions:

As we can see, only the positions of R and U remain unchanged. Thus, the positions of exactly Two persons remain unchanged.