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 person is five persons younger than the person whose age is equal to the sum of age of K and T?

To find the correct answer, let us analyze the given information step-by-step and determine the ages and birth years of all the eleven persons (K, L, M, N, O, P, Q, R, S, T, and U).

First, let us list the birth years given and calculate the age of each person as of the base year 2023:
- 1981: 2023 - 1981 = 42 years old
- 1983: 2023 - 1983 = 40 years old
- 1987: 2023 - 1987 = 36 years old
- 1994: 2023 - 1994 = 29 years old
- 1997: 2023 - 1997 = 26 years old
- 1999: 2023 - 1999 = 24 years old
- 2000: 2023 - 2000 = 23 years old
- 2003: 2023 - 2003 = 20 years old
- 2006: 2023 - 2006 = 17 years old
- 2007: 2023 - 2007 = 16 years old
- 2011: 2023 - 2011 = 12 years old

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

Now, let us apply the clues:
1. Age of L is a prime number: The prime numbers among the ages are 29, 23, and 17. So, L's age is either 29, 23, or 17.
2. The age difference between L and Q is 3 years:
- If L = 29, then Q could be 26 (difference of 3 years).
- If L = 23, then Q could be 26 or 20.
- If L = 17, then Q could be 20.
3. P is three persons younger than Q: This means P is younger than Q, and there are exactly 2 persons born between Q and P in the ordered list of years.
4. O is either five persons elder than L or five persons younger than L: This means O is 5 positions above or below L in the ordered list.
- If L is at 4th (age 29): O can only be at 9th (age 17) because there are not enough positions above 4th.
- If L is at 7th (age 23): O can be at 2nd (age 40).
- If L is at 9th (age 17): O can be at 4th (age 29).
5. The number of persons elder to O is one less than the number of persons younger to N: Let $x$ be the position of O (from oldest 1 to youngest 11). The number of persons elder to O is $x-1$. The number of persons younger to N must then be $x$. Therefore, N must be at position $12-x$.
- If O is 9th ($x=9$): N is 3rd (age 36).
- If O is 2nd ($x=2$): N is 10th (age 16).
- If O is 4th ($x=4$): N is 8th (age 20).
6. T is immediately younger to N:
- If N is 3rd, T is 4th (age 29).
- If N is 10th, T is 11th (age 12).
- If N is 8th, T is 9th (age 17).
7. The age difference between R and T is 13 years:
- If T = 29: R can be 42 (since 42 - 29 = 13). This works because 42 is one of the ages.
- If T = 12: R can be 25 (not in list).
- If T = 17: R can be 30 or 4 (neither in list).
Thus, T must be 29 (4th position), which means N is 3rd (age 36), O is 9th (age 17), and L is 4th (which is not possible since T is 4th. Wait, let's re-verify the case where O is 9th. If O is 9th, L must be 4th or 14th (invalid). But T is 4th, so L cannot be 4th).
Let us re-evaluate: If L is 7th (age 23): O is 2nd (age 40). Then N is 10th (age 16) and T is 11th (age 12). The age of T is 12, so R must be 12 + 13 = 25 (not in list).
What if L is 9th (age 17)? Then O can be 4th (age 29). Since O is 4th, N is 8th (age 20). T is immediately younger to N, so T is 9th (age 17). But L is also 9th (age 17), which is a contradiction.
Let's re-read: "O is either five persons elder than L or five persons younger than L."
If L is 7th (age 23), five persons elder than L is 7 - 5 = 2nd (age 40). If O is 2nd, the number of persons elder to O is 1. The number of persons younger to N is then 1 + 1 = 2. So N is 10th (age 16). T is immediately younger to N, so T is 11th (age 12). The age difference between R and T is 13 years, so R is 12 + 13 = 25, which is not in the list. Wait, what if R is younger than T? 12 - 13 is negative, so R must be 25. Let us look at other possibilities for L. What if L is 9th (age 17)? The prime numbers are 17, 23, 29. Let's check L = 23. If L is 7th, O can also be 7 + 5 = 12th (not possible). Wait, let's check: "The number of persons elder to O is one less than the number of persons younger to N." If O is 2nd, elder to O is 1 person. Number of persons younger to N is 2. So N is 10th (age 16). This means T is 11th (age 12). This gave R = 25. Let's check if there is another set of positions. What if O is 9th (age 17)? Elder to O is 8. Younger to N is 9. So N is 3rd (age 36). T is 4th (age 29). Age difference between R and T is 13. So R = 29 + 13 = 42 (which is 1st, age 42) or R = 29 - 13 = 16 (which is 10th, age 16). If O is 9th, L must be 5 persons elder or younger. Since O is 9th, L can be 4th (age 29). But T is 4th (age 29). This is a conflict. Wait! "O is either five persons elder than L or five persons younger than L." If L is 9th (age 17), five persons elder than L is 4th (age 29). So O is 4th. If O is 4th, the number of persons elder to O is 3. The number of persons younger to N is 3 + 1 = 4. So N is 8th (age 20). T is immediately younger to N, so T is 9th (age 17). But L is 9th. This is also a conflict. What if L is 29 (4th)? Five persons younger than L is 9th (age 17). So O is 9th. Elder to O is 8. Younger to N is 9. So N is 3rd (age 36). T is immediately younger to N, so T is 4th. But L is 4th. Conflict. Wait! Let's check the prime ages again: 29 (4th), 23 (7th), 17 (9th). Could L be 23 (7th)? "The age difference between L and Q is of 3 years." If L = 23 (7th): Case A: Q = 26 (5th). P is three persons younger than Q. Since Q is 5th, P is 8th (age 20). O is either five persons elder than L (2nd) or younger (12th - invalid). So O is 2nd (age 40). If O is 2nd, elder to O is 1. Younger to N is 2. So N is 10th (age 16). T is immediately younger to N, so T is 11th (age 12). The age difference between R and T is 13 years. R can be 12 + 13 = 25 (not in list). This case fails. Case B: Q = 20 (8th). P is three persons younger than Q, so P is 11th (age 12). O is 2nd (age 40). N is 10th (age 16). T is 11th (age 12). But P is 11th, conflict. Let's re-verify the prime numbers among the ages: Ages: 42, 40, 36, 29, 26, 24, 23, 20, 17, 16, 12. Primes: 29, 23, 17. What if T = 29 (4th)? R is 16 (10th) (since 29 - 16 = 13). Then N is 3rd (age 36). If N is 3rd, younger to N is 8. Elder to O is 8 - 1 = 7. So O is 8th (age 20). Since O is 8th, L must be 5 persons elder/younger, so L is 3rd (age 36) or 13th (invalid). But N is 3rd. Conflict. What if N is 5th (age 26)? Younger to N is 6. Elder to O is 5, so O is 6th (age 24). Then T is 6th (age 24). R is 24 + 13 = 37 (not in list) or 24 - 13 = 11 (not in list). Let's test all possible positions for O and N: If O = 1st (age 42): elder to O = 0. Younger to N = 1. N = 11th (age 12). T = cannot be younger. If O = 2nd (age 40): elder to O = 1. Younger to N = 2. N = 10th (age 16). T = 11th (age 12). R - T = 13 ⇒ R = 25 (no). If O = 3rd (age 36): elder to O = 2. Younger to N = 3. N = 9th (age 17). T = 10th (age 16). R - T = 13 ⇒ R = 29 (4th). Let's check this path: O is 3rd, N is 9th, T is 10th (age 16), R is 4th (age 29). L is either 5 persons elder or younger than O. Since O is 3rd, L must be 8th (age 20). Is L's age a prime number? L's age is 20, which is NOT prime. So this path fails. If O = 4th (age 29): elder to O = 3. Younger to N = 4. N = 8th (age 20). T = 9th (age 17). R - T = 13 ⇒ R = 30 or 4 (no). If O = 5th (age 26): elder to O = 4. Younger to N = 5. N = 7th (age 23). T = 8th (age 20). R - T = 13 ⇒ R = 33 or 7 (no). If O = 6th (age 24): elder to O = 5. Younger to N = 6. N = 6th (age 24) - but N and O cannot be the same. If O = 7th (age 23): elder to O = 6. Younger to N = 7. N = 5th (age 26). T = 6th (age 24). R - T = 13 ⇒ R = 37 or 11 (no). If O = 8th (age 20): elder to O = 7. Younger to N = 8. N = 4th (age 29). T = 5th (age 26). R - T = 13 ⇒ R = 39 (no) or 13 (no). If O = 9th (age 17): elder to O = 8. Younger to N = 9. N = 3rd (age 36). T = 4th (age 29). R - T = 13 ⇒ R = 42 (1st) or 16 (10th). Let's check R = 42 (1st). Since O is 9th, L can be 4th (but T is 4th) or L can be 14th (invalid). So this fails. What about R = 16 (10th)? Still L would need to be 4th (conflict with T). If O = 10th (age 16): elder to O = 9. Younger to N = 10. N = 2nd (age 40). T = 3rd (age 36). R - T = 13 ⇒ R = 23 (7th) (since 36 - 23 = 13). Since O is 10th, L must be 5 persons elder than O ⇒ L is 5th (age 26). But L must be prime, and 26 is not prime. So this fails. If O = 11th (age 12): elder to O = 10. Younger to N = 11. N = 1st (age 42). T = 2nd (age 40). R - T = 13 ⇒ R = 27 (no). Wait, let's re-read: "Age of L is a prime number." Is it possible that the order is from youngest to oldest? Let's check: "O is either five persons elder than L or five persons younger than L." "Elder" and "younger" refer to age. "P is three persons younger than Q." "The number of persons elder to O is one less than the number of persons younger to N." "T is immediately younger to N." If N's age is 16 (10th), T (immediately younger to N) is 11th (age 12). Wait, if R = 23 (7th) and T = 36 (3rd), the difference is 13 years! Let's check if N = 2nd (age 40), then T = 3rd (age 36), and R = 23 (7th). Let's look at the statement: "The number of persons elder to O is one less than the number of persons younger to N." If O is 10th (age 16): number of persons elder to O is 9. Number of persons younger to N (where N is 2nd, age 40) is 9. So "one less than the number of persons younger to N" is 9 - 1 = 8. But number of persons elder to O is 9. This does not match (9 is not equal to 8). Let's check the formula: Number of persons elder to O = $\text{Position of O}-1$. Number of persons younger to N = $11-\text{Position of N}$. So: $\text{Position of O}-1=(11-\text{Position of N})-1$ $\Rightarrow \text{Position of O}-1=10-\text{Position of N}$ $\Rightarrow \text{Position of O}+\text{Position of N}=11$. Let's re-verify with this: - If O is 10th, N must be 1st. Then T is 2nd. R - T = 13 ⇒ R - 40 = 13 (no) or 40 - R = 13 ⇒ R = 27 (no). - If O is 9th, N is 2nd (age 40). T is 3rd (age 36). R - T = 13 ⇒ R = 23 (7th) or R = 49 (no). Let's check this case: O is 9th (age 17), N is 2nd (age 40), T is 3rd (age 36), R is 7th (age 23). Since O is 9th, L (being 5 persons elder or younger) must be 4th (age 29) or 14th (invalid). Let's check L = 4th (age 29). Is 29 prime? Yes! So L = 29 (4th). Now let's check other clues: - "The age difference between L and Q is of 3 years." Since L is 29 (4th), Q can be 26 (5th) because 29 - 26 = 3. - "P is three persons younger than Q." Since Q is 5th, P is 5 + 3 = 8th (age 20). - "R is not immediately elder to Q." R is 7th, Q is 5th. R is younger than Q, so this is satisfied. - "Age of M is completely divisible by 4 and is elder to K." Divisible by 4 ages are: 40 (N), 36 (T), 24, 20 (P), 16, 12. Since N is 40, T is 36, P is 20, the remaining ages divisible by 4 are 24, 16, 12. - "S is 2 years elder to K." Looking at the remaining ages: 42, 26, 24, 16, 12. Pairs with difference of 2 years: (26, 24) and (14 - not in list) and (18, 16 - 18 not in list) and (12, 14). So S must be 26 (5th) and K must be 24 (6th). Wait, but Q was 26 (5th)! Let's check: Q and S cannot both be 26. Is there another age difference of 2? Ages are: 42, 40, 36, 29, 26, 24, 23, 20, 17, 16, 12. Difference of 2: - 42 and 40 (N is 40) - 26 and 24 - 18 and 16 (no 18) - 14 and 12 (no 14) So the only available pair with difference 2 is 26 and 24. Thus, S = 26 and K = 24. Since S is 26, Q cannot be 26. But L = 29, so Q must be 26. This is a conflict. Wait, can Q be 32? (not in list). Let's check the age difference between L and Q: "The age difference between L and Q is of 3 years." If L = 23 (7th): Then Q = 20 (8th) or 26 (5th). If Q = 20 (8th), then P (three persons younger than Q) is 11th (age 12). If L is 7th, O is 2nd (age 40). Then N is 9th (age 17) [since Position of O + Position of N = 11 ⇒ 2 + 9 = 11]. T is immediately younger to N, so T is 10th (age 16). The age difference between R and T is 13 years ⇒ R - T = 13 ⇒ R = 16 + 13 = 29 (4th). Let's check this set: 1. 42 (1981) 2. O (40, 1983) 3. 36 (1987) 4. R (29, 1994) 5. 26 (1997) 6. 24 (1999) 7. L (23, 2000) 8. Q (20, 2003) 9. N (17, 2006) 10. T (16, 2007) 11. P (12, 2011) Let's check: "R is not immediately elder to Q." R is 4th, Q is 8th. Satisfied. Now for M, K, S: Remaining positions: 1st (42), 3rd (36), 5th (26), 6th (24). "S is 2 years elder to K." Using remaining positions: - S = 26 (5th), K = 24 (6th) - Difference is 2 years (26 - 24 = 2). - M must be elder to K and divisible by 4. Remaining positions for M: 1st (42), 3rd (36). Both 42 and 36 are elder to K (24). But M's age must be completely divisible by 4. - 42 is not divisible by 4. - 36 is divisible by 4. So M = 36 (3rd). Then U must be the remaining person: U = 42 (1st). This fits all conditions perfectly! Let's double-check the final ages of all persons: - 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 Let's check the question: "Who among the following person is five persons younger than the person whose age is equal to the sum of age of K and T?" - Age of K = 24 - Age of T = 16 - Sum of ages of K and T = 24 + 16 = 40. - The person whose age is 40 is O (at position 2). - The person who is five persons younger than O: Position of O (2nd) + 5 = 7th position. - The person at the 7th position is L. Therefore, L is the correct answer.