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.

M was born in which year?

Correct Answer: 1980

Step-by-step Explanation:

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

• Year 1955: Age = 2024 - 1955 = 69 years

• Year 1967: Age = 2024 - 1967 = 57 years

• Year 1973: Age = 2024 - 1973 = 51 years

• Year 1980: Age = 2024 - 1980 = 44 years

• Year 1987: Age = 2024 - 1987 = 37 years

• Year 1991: Age = 2024 - 1991 = 33 years

• Year 2003: Age = 2024 - 2003 = 21 years

Step 2: Determine the position of L and Q.

The problem states: "L’s age is multiple of 3."

The ages that are multiples of 3 are: 69, 57, 51, 33, and 21.

Also, "Three persons were born between L and Q."

Let's check the possible positions for L and Q:

• If L is born in 1955 (age 69 - 1st person), then Q must be the 5th person, born in 1987 (age 37).

• If L is born in 1967 (age 57 - 2nd person), then Q must be the 6th person, born in 1991 (age 33).

• If L is born in 1973 (age 51 - 3rd person), then Q must be the 7th person, born in 2003 (age 21).

• If L is born in 1991 (age 33 - 6th person), then Q must be the 2nd person, born in 1967 (age 57).

• If L is born in 2003 (age 21 - 7th person), then Q must be the 3rd person, born in 1973 (age 51).

Step 3: Use the condition for P and K.

"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."

Let's test the possibility where Q's age has a 12-year difference with another available age:

Look at the age differences available:

• 69 - 57 = 12 years

• 33 - 21 = 12 years

• 69 - 37 = 32 (not 12)

• 57 - 45 (not in list)

• 51 - 39 (not in list)

Case A: Q's age is 57 (born in 1967, 2nd person).

Then K's age must be 69 (born in 1955).

If Q is born in 1967 (2nd person, so 1 person born before Q), then P must be the 6th person, born in 1991 (so 1 person born after P).

Since Q is born in 1967, L must be born in 1991 (3 persons between L and Q). But P is already in 1991, which creates a conflict.

Case B: Q's age is 33 (born in 1991, 6th person).

Then K's age must be 21 (born in 2003) or 45 (not available). So K = 21 (born in 2003).

If Q is born in 1991 (6th person, so 5 persons born before Q), then P must be the 2nd person, born in 1967 (so 5 persons born after P).

Since Q is born in 1991 (6th person), L must be born in 1967 (2nd person). But P is already in 1967, which creates a conflict.

Case C: Q's age is 21 (born in 2003, 7th person).

Then K's age must be 21 + 12 = 33 (born in 1991).

If Q is the 7th person (born in 2003), there are 6 persons born before Q, so P must be the 1st person, born in 1955 (6 persons born after P).

Since Q is the 7th person (2003), L must be the 3rd person, born in 1973 (3 persons between L and Q: 1980, 1987, 1991).

L's age is 51, which is a multiple of 3. This condition is satisfied!

So far, we have:

• 1955 (69 years): P

• 1967 (57 years): [Empty]

• 1973 (51 years): L

• 1980 (44 years): [Empty]

• 1987 (37 years): [Empty]

• 1991 (33 years): K

• 2003 (21 years): Q

Step 4: Place M, N, and O.

The remaining vacant years are: 1967 (57 yrs), 1980 (44 yrs), and 1987 (37 yrs).

The condition says: "M is 7 years older to N."

Looking at the ages for the vacant years: 44 - 37 = 7 years!

Therefore, M's age is 44 years (born in 1980) and N's age is 37 years (born in 1987).

The remaining year 1967 (57 years) is filled by O.

Condition check: "N is younger to O." -> N (37 years) is indeed younger than O (57 years).

Final Arrangement:

• 1955: P

• 1967: O

• 1973: L

• 1980: M

• 1987: N

• 1991: K

• 2003: Q

Thus, M was born in the year 1980.