Read the given information carefully and answer the related questions:

Seven persons was born on same date and same month but in different years – 1955, 1967, 1973 1980, 1987, 1991, 2003. Consider the base year 2024 to calculate the ages.

L’s age is multiple of 3. Three persons were born between L and Q. Number of persons born before Q is same as the number of persons born after P . Difference between the age of Q and K is 12 years. M is 7 years older to N. N is younger to O.

If P is related to L, N is related to Q, then M is related to ___.

The correct option is K.

Step 1: Calculate the age of each person considering the base year 2024.

Let's find the age of a person born in each year by subtracting the birth year from 2024:

• 1955: 2024 - 1955 = 69 years old
• 1967: 2024 - 1967 = 57 years old
• 1973: 2024 - 1973 = 51 years old
• 1980: 2024 - 1980 = 44 years old
• 1987: 2024 - 1987 = 37 years old
• 1991: 2024 - 1991 = 33 years old
• 2003: 2024 - 2003 = 21 years old

Step 2: Determine the positions of the seven persons from oldest to youngest.

1. L's age is a multiple of 3:
The ages that are multiples of 3 are 69, 57, 51, 33, and 21.

2. Three persons were born between L and Q:
• If L is born in 1955 (age 69), Q must be born in 1987 (age 37).
• If L is born in 1967 (age 57), Q must be born in 1991 (age 33).
• If L is born in 1973 (age 51), Q must be born in 2003 (age 21).
• If L is born in 1987 (age 37), 37 is not a multiple of 3.
• If L is born in 1991 (age 33), Q must be born in 1967 (age 57).
• If L is born in 2003 (age 21), Q must be born in 1973 (age 51).

3. Difference between the age of Q and K is 12 years:
• If Q is born in 1987 (age 37), K's age would be 37 + 12 = 49 (not present) or 37 - 12 = 25 (not present). So Q cannot be 37.
• If Q is born in 1973 (age 51), K's age would be 51 + 12 = 63 (not present) or 51 - 12 = 39 (not present). So Q cannot be 51.
• If Q is born in 1991 (age 33), K's age would be 33 + 12 = 45 (not present) or 33 - 12 = 21 (born in 2003, valid).
Thus, Q is born in 1991 (age 33), L is born in 1967 (age 57), and K is born in 2003 (age 21).

4. Number of persons born before Q is same as the number of persons born after P:
Q is born in 1991 (5th position from oldest to youngest). There are 5 persons born before Q (1955, 1967, 1973, 1980, 1987).
Therefore, 5 persons must be born after P, placing P in the 2nd position, which is the year 1967.
Wait, L is already at 1967. Let's re-count positions:
Years: 1955 (1st), 1967 (2nd), 1973 (3rd), 1980 (4th), 1987 (5th), 1991 (6th), 2003 (7th).
• Q is born in 1991, which has 5 persons born before Q.
• So 5 persons are born after P, meaning P is born in 1967.
Wait, if L is born in 2003 (age 21), Q is born in 1973 (3rd position).
Let's re-verify Q = 1991 (age 33):
K's age = 33 + 12 = 45 (No) or 33 - 12 = 21 (Yes, K = 2003).
If Q is born in 1991 (6th year), 5 people are born before Q. Then 5 people must be after P, so P is 2nd year (1967). But L and P cannot both be 1967.
Let's check Q = 1980 (age 44):
Age difference with K is 12: 44 + 12 = 56 (No), 44 - 12 = 32 (No).
Let's check Q = 1987 (age 37):
Difference of Q and K is 12: 37 + 12 = 49 (No).
Let's check Q = 1967 (age 57):
L is 1991 (age 33). Q is 1967 (age 57).
Difference between Q (57) and K is 12 years: 57 + 12 = 69 (born in 1955, valid!).
So Q is born in 1967 (age 57), K is born in 1955 (age 69), L is born in 1991 (age 33).

Let's check this arrangement:
• Q is born in 1967 (2nd position). 1 person is born before Q.
• Therefore, 1 person is born after P, so P is born in 1991 (6th position). But L is 1991! Wait, let's check P = 1991.
Wait, let's re-verify Q = 1980, age 44, 44+12=56 (no).
Let's re-verify Q = 2003 (age 21):
Difference between Q and K is 12: 21 + 12 = 33 (born in 1991, valid!).
So Q is born in 2003 (7th position), K is born in 1991 (6th position).
Since 3 persons are born between L and Q:
L is born in 1980 (4th position). But 44 is NOT a multiple of 3.
Wait, between 2003 (7th) and 1973 (3rd), there are 3 persons (1980, 1987, 1991). So L is born in 1973 (age 51, which IS a multiple of 3: 51 / 3 = 17)!
Let's check:
• L is born in 1973 (age 51 - multiple of 3).
• 3 persons between L (1973) and Q (2003): 1980, 1987, 1991. So Q is born in 2003.
• Persons born before Q (2003): 6 persons (1955, 1967, 1973, 1980, 1987, 1991).
• Persons born after P: must also be 6, so P is born in 1955 (1st position).
• Difference between age of Q (21) and K is 12 years: K's age = 21 + 12 = 33 years (born in 1991).
• M is 7 years older than N: Ages available are 1967 (57), 1980 (44), 1987 (37).
The difference 44 - 37 = 7! So M's age is 44 (born in 1980) and N's age is 37 (born in 1987).
• Remaining position 1967 (age 57) goes to O.
• N (born in 1987, age 37) is younger than O (born in 1967, age 57), which is correct!

Step 3: Final Birth Year Mapping

• 1955 (69 years): P
• 1967 (57 years): O
• 1973 (51 years): L
• 1980 (44 years): M
• 1987 (37 years): N
• 1991 (33 years): K
• 2003 (21 years): Q

Step 4: Find the pattern for the question

Looking at the positions in the ordered list [P, O, L, M, N, K, Q]:
• P (1st) is related to L (3rd) → (+2 positions)
• N (5th) is related to Q (7th) → (+2 positions)
• Following the same pattern, M (4th) is related to the person 2 positions after M, which is K (6th).

Therefore, M is related to K.