Directions: Read the following information carefully and answer the question given below.

Seven individuals — K, L, M, N, O, P, and Q — were born in seven different years: 1954, 1962, 1970, 1980, 1991, 1998, and 2007, on the same month and day. (Consider 2024 as the base year for age calculations). The combined age of P and Q is equal to the age of O. P's age is an even number divisible by 13. K is immediately older than P. L's age is a multiple of 9. M is older than N.

What is the age of L?

The correct option is 54 years.

Step 1: Calculate the age of each individual for the base year 2024.
Using the formula (Age = 2024 - Birth Year):
• 2024 - 1954 = 70 years
• 2024 - 1962 = 62 years
• 2024 - 1970 = 54 years
• 2024 - 1980 = 44 years
• 2024 - 1991 = 33 years
• 2024 - 1998 = 26 years
• 2024 - 2007 = 17 years

The set of available ages in descending order is: {70, 62, 54, 44, 33, 26, 17}.

Step 2: Determine P's age and K's age.
• P's age is an even number divisible by 13. Among the available ages, 26 is even and divisible by 13 (26 = 2 × 13). Thus, P = 26 years.
• K is immediately older than P. In the ordered age list, the age immediately greater than 26 is 33. Thus, K = 33 years.

Step 3: Determine O's age and Q's age.
• The combined age of P and Q equals the age of O (P + Q = O).
Substituting P = 26:
26 + Q = O
Testing available remaining ages {70, 62, 54, 44, 17}:
If Q = 44, then O = 26 + 44 = 70, which exists in our age set.
Thus, Q = 44 years and O = 70 years.

Step 4: Determine L's age.
• L's age is a multiple of 9.
The remaining ages are {62, 54, 17}.
Among these, 54 is divisible by 9 (54 = 6 × 9).
Thus, L = 54 years.

Step 5: Determine M's age and N's age.
• M is older than N.
The remaining ages are 62 and 17.
Thus, M = 62 years and N = 17 years.

Summary of Ages:
• O = 70 years (1954)
• M = 62 years (1962)
• L = 54 years (1970)
• Q = 44 years (1980)
• K = 33 years (1991)
• P = 26 years (1998)
• N = 17 years (2007)

Therefore, the age of L is 54 years.