Read the given information carefully and answer the question that follows:…

Concept

In a 'born in different years' puzzle, arrange the people on a single timeline from oldest (earliest year) to youngest (latest year). Convert every age clue into a year clue using birth year = base year - age, and read 'older' as an earlier year and 'younger' as a later year. Apply the clues together, eliminating placements that violate any one of them, until a single arrangement survives.

Setting up

Years available: 1955, 1967, 1973, 1980, 1987, 1991, 2003. With base year 2024 the ages are 69, 57, 51, 44, 37, 33 and 21 respectively. We fill seven slots from oldest to youngest.

Applying the clues

1. L's age is a multiple of 3. Of the ages 69, 57, 51, 44, 37, 33, 21, the multiples of 3 are 69, 57, 51, 33 and 21 - so L is one of 1955, 1967, 1973, 1991 or 2003 (only 1980 and 1987 are excluded for L).

2. Three persons are born between L and Q, so L and Q sit four slots apart on the timeline. Combined with the next clues this fixes L = 1973 and Q = 2003: the four-slot span 1973 ... 2003 leaves exactly three people in between, and the other multiple-of-3 choices for L cannot keep all later clues consistent.

3. The number of persons born before Q equals the number born after P. Q is youngest (slot 7), so six people are born before Q; six must then be born after P, which is only possible if P is the oldest, born in 1955.

4. The difference between the ages of Q and K is 12 years, so their birth years differ by 12. Q = 2003, hence K = 1991 (2003 - 1991 = 12); 2003 + 12 = 2015 is not in the list.

5. M is 7 years older than N (M's year is 7 less than N's), and N is younger than O (N born after O). The three years still unused are 1967, 1980 and 1987. Only M = 1980 with N = 1987 gives the required 7-year gap, and that forces O = 1967, which correctly leaves N younger than O. No other split of these three years satisfies both clues.

6. Consistency check on L: had L been 1955, 1967, 1991 or 2003 instead of 1973, the four-slot L-Q span would either run off the timeline or leave Q with no valid 12-year partner for K, or force P out of the oldest slot - so L = 1973 is the only multiple-of-3 placement that survives.

Final timeline (oldest to youngest)

Cross-check

• Between L (1973) and Q (2003) sit M, N, K - exactly three persons. Correct.

• Persons before Q = 6, persons after P = 6. Equal. Correct.

• Q and K year gap = 2003 - 1991 = 12. Correct.

• M (1980) is 7 years older than N (1987), and N (1987) is younger than O (1967). Correct.

Result

M was born in 1980.