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 analyze the clues step-by-step to reconstruct the floor plan.

The building has 5 floors (numbered 1 to 5 from bottom to top) and two flats on each floor: Flat 1 (West) and Flat 2 (East).

Step 1: Place P and S
According to the clues, P lives in Flat 2 of the topmost floor (Floor 5). Therefore, P is on Floor 5, Flat 2.
S lives to the west of P, which means S must be on Floor 5, Flat 1.
Floor 5 is now fully occupied: Floor 5 = [S (Flat 1), P (Flat 2)].

Step 2: Analyze L, N, and Q
L lives on an even-numbered floor in Flat 1. Since Floor 5 is full, the even floors available for L are Floor 4 and Floor 2.
N lives immediately below L's floor in Flat 1, and N is west of Q (which means Q is in Flat 2 of the same floor as N).
Let us evaluate the two cases for L:
• Case A: If L is on Floor 4 (Flat 1), then N and Q are on Floor 3 (N in Flat 1, Q in Flat 2).
• Case B: If L is on Floor 2 (Flat 1), then N and Q are on Floor 1 (N in Flat 1, Q in Flat 2).

Step 3: Analyze K and O
K and L live in different named flats. Since L is in Flat 1, K must be in Flat 2.
K and R live in the same named flat, so R is also in Flat 2.
Only one floor is between K and O, and K lives below O. This means O is exactly two floors above K (Floor of O = Floor of K + 2).

Step 4: Analyze M and J
M lives immediately below O, but in a different named flat.
One floor is between J's floor and L's floor.

Step 5: Testing Case A (L on Floor 4, Flat 1)
If L is on Floor 4, then N is on Floor 3, Flat 1 and Q is on Floor 3, Flat 2.
Since there is one floor between J and L, J must be on Floor 2 (as Floor 5 is occupied).
Now let's place K (Flat 2) and O. Since O is two floors above K:
If K is on Floor 2 (Flat 2), O must be on Floor 4 (Flat 2, since Floor 4 Flat 1 has L).
If O is on Floor 4, Flat 2, then M (who lives immediately below O in a different flat) must live on Floor 3, Flat 1. However, Floor 3, Flat 1 is already occupied by N. Thus, Case A is invalid.

Step 6: Testing Case B (L on Floor 2, Flat 1)
If L is on Floor 2, then N is on Floor 1, Flat 1 and Q is on Floor 1, Flat 2.
Since there is one floor between J and L, J must be on Floor 4 (as Floor 5 is occupied).
Now let's place K (Flat 2) and O. Since O is two floors above K, K must be on Floor 2, Flat 2, and O must be on Floor 4.
Since J is on Floor 4, and O is on Floor 4, we have:
Floor 4 = [J (Flat 1), O (Flat 2)] or [O (Flat 1), J (Flat 2)].
Let's place M, who lives immediately below O (Floor 3) in a different flat:
If O is on Floor 4, Flat 2, then M must be on Floor 3, Flat 1.
This leaves Floor 3, Flat 2 for R (since R must be in Flat 2). This is consistent with all constraints!

Final Arrangement:
• Floor 5: S (Flat 1), P (Flat 2)
• Floor 4: J (Flat 1), O (Flat 2)
• Floor 3: M (Flat 1), R (Flat 2)
• Floor 2: L (Flat 1), K (Flat 2)
• Floor 1: N (Flat 1), Q (Flat 2)

From this arrangement, we can see that K and L both live on Floor 2.