Ten people—J, K, L, M, N, O, P, Q, R, and S —live in a building with five floors and two flats (Flat 1 and Flat 2) on each floor. The floors are numbered from 1 to 5 (1 being the lowermost floor and 5 being the topmost floor).

Note I: Each floor has two flats viz., Flat-1 and Flat-2, where Flat 1 is to the west of Flat 2.

Note II: Flat 1 of floor 2 is immediately above Flat 1 of floor 1 and immediately below Flat 1 of floor 3 and so on. Similarly Flat 2 of floor 2 is immediately above Flat 2 of floor 1 and immediately below Flat 2 of floor 3 and so on.

Note III: The area of each flat is equal.

Note IV: Only two persons live on each floor and only one person lives in each flat.

L lives on an even -numbered floor in Flat -1. P lives in Flat -2 of the topmost floor. N lives west of Q. N lives on a floor immediately below the L’s floor. K and R live on the same named flat. K and L lives in a different named flat. Only one floor is between K and O. K lives below O. S lives to the west of P. M lives immediately below O, but not in the same named flat. One floor between J’s floor and L’s floor.

Which pair of people live on the same floor?

To find the pair of people who live on the same floor, we can construct the floor and flat arrangement step-by-step based on the given clues.

The building has 5 floors (numbered 1 to 5 from bottom to top) and 2 flats on each floor (Flat 1 to the west, Flat 2 to the east).

Step 1: Place S and P on the topmost floor.
- P lives in Flat 2 of the topmost floor (Floor 5).
- S lives to the west of P, which means S lives in Flat 1 of Floor 5.
So, Floor 5: Flat 1 = S, Flat 2 = P.

Step 2: Locate L, N, and Q.
- L lives on an even-numbered floor (Floor 2 or Floor 4) in Flat 1.
- N lives on the floor immediately below L's floor, and N lives to the west of Q (meaning N is in Flat 1 and Q is in Flat 2).
Let's analyze the two possibilities for L:
- Case 1: If L lives on Floor 4, then N and Q must live on Floor 3. But we also have a clue: "One floor between J's floor and L's floor." Since Floor 5 is full, J's floor would have to be Floor 2.
- Case 2: If L lives on Floor 2, then N and Q must live on Floor 1. Consequently, J's floor must be Floor 4 (since Floor 5 is full and there must be one floor between J and L).

Step 3: Analyze K and O's positions.
- K and L live in different named flats. Since L is in Flat 1, K must live in Flat 2.
- K and R live in the same named flat, so R also lives in Flat 2.
- Only one floor is between K and O, and K lives below O (so O is two floors above K).
Let's test our cases with these conditions:
- In Case 1 (L on Floor 4, J on Floor 2, N & Q on Floor 3):
If K is on Floor 1, O must be on Floor 3. But Floor 3 is fully occupied by N and Q. If K is on Floor 2 (Flat 2), O must be on Floor 4 (Flat 2). Then, M lives immediately below O (Floor 3) but in a different flat than O. Since O is in Flat 2, M must be in Flat 1. However, Floor 3, Flat 1 is already occupied by N. Thus, Case 1 is invalid.
- In Case 2 (L on Floor 2, J on Floor 4, N & Q on Floor 1):
Since Floor 1 is occupied by N and Q, K cannot be on Floor 1. Since Floor 5 is occupied by S and P, K cannot be on Floor 3 (as O would have to be on Floor 5). Thus, K must be on Floor 2 (Flat 2), and O must be on Floor 4.

Step 4: Finalize the arrangements.
- Since K is on Floor 2, Flat 2 and L is on Floor 2, Flat 1, they live on the same floor.
- Since O is on Floor 4 and J is on Floor 4, they occupy Floor 4.
- M lives immediately below O (Floor 3) but not in the same named flat as O. R (who is in Flat 2) must occupy the remaining spot on Floor 3. This puts R in Floor 3, Flat 2 and M in Floor 3, Flat 1. This means O must be in Floor 4, Flat 2 and J in Floor 4, Flat 1.

The complete arrangement is:
- Floor 5: Flat 1 = S, Flat 2 = P
- Floor 4: Flat 1 = J, Flat 2 = O
- Floor 3: Flat 1 = M, Flat 2 = R
- Floor 2: Flat 1 = L, Flat 2 = K
- Floor 1: Flat 1 = N, Flat 2 = Q

Therefore, the pair of people who live on the same floor is K and L (on Floor 2).