Read the given information carefully and answer the related questions:

Seven persons K, L, M, N, O, P and Q - were born (not in given order) on same date of same month but in different year – 1955, 1961, 1972, 1987, 1998, 2006, 2017. Consider base year 2025 for age calculation.

M’s age is the cube of a number. 11 years difference between M and K. Three persons are in between K and P. N is 32 years older to Q. L’s age is the cube of a number. Age difference between L and K is more than 10 years.

What is the age difference between N and K?

The correct answer is 17 years.

Let's first calculate the age of each person in the base year 2025 based on their birth years:
- Born in 1955: 2025 - 1955 = 70 years old
- Born in 1961: 2025 - 1961 = 64 years old
- Born in 1972: 2025 - 1972 = 53 years old
- Born in 1987: 2025 - 1987 = 38 years old
- Born in 1998: 2025 - 1998 = 27 years old
- Born in 2006: 2025 - 2006 = 19 years old
- Born in 2017: 2025 - 2017 = 8 years old

Arranging the ages in descending order, we have: 70, 64, 53, 38, 27, 19, 8.

Step 1: Determine the ages of M and K
M’s age is a perfect cube. The perfect cubes among the available ages are:
$8=2^3$
$27=3^3$
$64=4^3$
The difference between M and K is 19 - 8 = 11, 38 - 27 = 11, or 64 - 53 = 11. This gives us three possible pairs for (M, K):
- (8, 19)
- (27, 38)
- (64, 53)

Step 2: Use the position of P to narrow down the cases
Three persons are born between K and P. In our sorted list of ages:
- If K is 38 (4th position), P cannot be placed since we need 3 people between them.
- If K is 19 (6th position), P must be 64 (2nd position).
- If K is 53 (3rd position), P must be 8 (7th position).

Step 3: Analyze the age difference between N and Q
N is 32 years older than Q. Looking at the ages, the only pair with a difference of 32 is 70 and 38:
- N = 70
- Q = 38

Step 4: Determine L's age and check constraints
Let's evaluate the remaining two valid configurations:
- Case A: K = 19, P = 64, N = 70, Q = 38, M = 8. This leaves the ages 53 and 27. Since L's age must be a perfect cube, L = 27. However, the age difference between L (27) and K (19) is 8 years, which violates the condition that the difference must be more than 10 years.
- Case B: K = 53, P = 8, N = 70, Q = 38, M = 64. This leaves the ages 27 and 19. Since L's age must be a perfect cube, L = 27. The age difference between L (27) and K (53) is 26 years, which is indeed more than 10 years. The remaining person O is 19 years old. This configuration is fully valid.

Step 5: Calculate the age difference between N and K
- N's age = 70 years
- K's age = 53 years
Difference:
$70-53=17\text{years}$