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.

Who among the following is 12 years elder than K?

First, let us calculate the age of each person by using the base year 2023:
- 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

Ordering the ages from oldest to youngest gives the following ranks:
1. 42 years (1981)
2. 40 years (1983)
3. 36 years (1987)
4. 29 years (1994)
5. 26 years (1997)
6. 24 years (1999)
7. 23 years (2000)
8. 20 years (2003)
9. 17 years (2006)
10. 16 years (2007)
11. 12 years (2011)

Now, let us analyze the clues step-by-step:
1. Age of L is a prime number: The prime numbers in the list of ages are 29, 23, and 17. Thus, L can be 29, 23, or 17.
2. The age difference between L and Q is of 3 years: Let us find pairs with a difference of 3 where L is prime:
- If L = 29, then Q = 26.
- If L = 23, then Q = 26 or Q = 20.
- If L = 17, then Q = 20.
3. P is three persons younger than Q: This means if Q is at rank r, P is at rank $r+3$.
- If L = 29, Q = 26 (rank 5), then P is rank 8 (20 years).
- If L = 23, Q = 26 (rank 5), then P is rank 8 (20 years).
- If L = 23, Q = 20 (rank 8), then P is rank 11 (12 years).
- If L = 17, Q = 20 (rank 8), then P is rank 11 (12 years).

4. O is either 5 persons elder or 5 persons younger than L:
- For L = 29 (rank 4): O must be rank 9 (17 years).
- For L = 23 (rank 7): O must be rank 2 (40 years).
- For L = 17 (rank 9): O must be rank 4 (29 years).
5. The number of persons elder to O is one less than the number of persons younger to N:
- If O is rank 9 (17 years, 8 persons elder), then N must have 9 persons younger, making N rank 2 (40 years).
- If O is rank 2 (40 years, 1 person elder), then N must have 2 persons younger, making N rank 9 (17 years).
- If O is rank 4 (29 years, 3 persons elder), then N must have 4 persons younger, making N rank 7 (23 years).

6. T is immediately younger to N:
- If N is rank 2, then T is rank 3 (36 years).
- If N is rank 9, then T is rank 10 (16 years).
- If N is rank 7, then T is rank 8 (20 years). (This conflicts with Q being rank 8 in the L = 17 case).

7. The age difference between R and T is 13 years:
- If T = 36 (Case 1), then R can be $36-13=23$ years.
- If T = 16 (Case 2 and Case 3), then R can be $16+13=29$ years.

8. R is not immediately elder to Q:
- In Case 2 (L = 23, Q = 26, R = 29), R is immediately elder to Q (since R is rank 4 and Q is rank 5). This violates the condition, so Case 2 is eliminated.
- In Case 1 (L = 29, Q = 26, R = 23), R is rank 7 and Q is rank 5. This is valid.
- In Case 3 (L = 23, Q = 20, R = 29), R is rank 4 and Q is rank 8. This is valid.

9. S is 2 years elder to K, and M's age is divisible by 4 and is elder to K:
- Testing Case 1: The remaining vacant ages are 42, 24, 16, and 12. No two vacant ages have a difference of 2 years to satisfy S and K. Hence, Case 1 is eliminated.
- Testing Case 3: The remaining vacant ages are 42, 36, 26, and 24. Here, we have 26 and 24 with a difference of 2. So, S = 26 years and K = 24 years.
The remaining vacant ages are 42 and 36. Since M's age is divisible by 4, M = 36 years. This leaves U = 42 years.

The final arrangement is:
- U: 42 years
- O: 40 years
- M: 36 years
- R: 29 years
- S: 26 years
- K: 24 years
- L: 23 years
- Q: 20 years
- N: 17 years
- T: 16 years
- P: 12 years

We need to find who is 12 years elder than K:
Age of K = 24 years.
Age of the person who is 12 years elder = $24+12=36$ years (which is M).
Looking at the options, the one who is immediately elder than R (29 years) is M (36 years).