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.

What is age difference between M and Q?

The correct answer is 23 years.

Step-by-step Explanation:

1. Calculate the age of each person based on the year 2024:

• Year 1955: 2024 - 1955 = 69 years old

• Year 1967: 2024 - 1967 = 57 years old

• Year 1973: 2024 - 1973 = 51 years old

• Year 1980: 2024 - 1980 = 44 years old

• Year 1987: 2024 - 1987 = 37 years old

• Year 1991: 2024 - 1991 = 33 years old

• Year 2003: 2024 - 2003 = 21 years old

2. Determine the position of L and Q:

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

L’s age is a multiple of 3. Also, three persons were born between L and Q.

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

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

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

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

3. Use the condition for P and Q:

The number of persons born before Q is the same as the number of persons born after P.

Let's test the case where Q is born in 1987 (age 37):

Q is the 5th person (4 persons born before Q). So, P must be the 3rd person (4 persons born after P), which means P was born in 1973 (age 51).

4. Determine the position of K:

Difference between the age of Q and K is 12 years.

Age of Q = 37 years.

• 37 + 12 = 49 years (not present in the list)

• 37 - 12 = 25 years (not present in the list)

Let's test another valid case: Q was born in 1991 (age 33) and L was born in 1967 (age 57).

• Since Q is the 6th person (5 persons born before Q), P must be the 2nd person (5 persons born after P), so P was born in 1967. But L is already born in 1967, so this case is invalid.

Let's test: Q was born in 1967 (age 57) and L was born in 1991 (age 33).

• Q is the 2nd person (1 person born before Q: in 1955). So, P is the 6th person (1 person born after P: in 2003), which means P was born in 1991. But L is already born in 1991, so this is invalid.

Let's test: Q was born in 1973 (age 51) and L was born in 2003 (age 21).

• Q is the 3rd person (2 persons born before Q). Therefore, P must be the 5th person (2 persons born after P), so P was born in 1987 (age 37).

• Age of Q = 51 years.

Difference between age of Q and K is 12 years:

Age of K = 51 + 12 = 63 (not in list) or 51 - 12 = 39 (not in list).

Wait, let's re-check the difference between Q and K: 12 years.

Looking at available ages: 69, 57, 51, 44, 37, 33, 21.

The pairs of ages with a difference of 12 years are:

• 69 - 57 = 12

• 45 is not there, 33 + 12 = 45 (no)

• 33 - 21 = 12

So the pair (Q, K) must be either (69, 57) or (33, 21).

Case 1: Q is 21 (born in 2003) and K is 33 (born in 1991).

Q is the 7th person (6 before Q) ⇒ P is the 1st person (6 after P, born in 1955).

Three persons between L and Q ⇒ L is the 3rd person (born in 1973, age 51 - multiple of 3).

Now remaining years to fill: 1967 (57), 1980 (44), 1987 (37).

M is 7 years older than N: 44 - 37 = 7 years. So M = 44 (born in 1980) and N = 37 (born in 1987).

N is younger than O: Remaining year for O is 1967 (age 57). Since 37 < 57, N (37) is younger than O (57). This satisfies all conditions!

Final Arrangement by birth year:

• 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

5. Calculate the age difference between M and Q:

Age of M = 44 years

Age of Q = 21 years

Difference = 44 - 21 = 23 years.