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.

Who lives in Flat 2 on the third floor?

Based on the provided information, the correct answer is R.

Let us break down the step-by-step derivation to find the positions of all ten people on the 5 floors (each having Flat 1 to the west and Flat 2 to the east):

Step 1: Place S and P on the 5th floor
According to the clues:

• P lives in Flat 2 of the topmost floor (Floor 5).
• S lives to the west of P. Since Flat 1 is to the west of Flat 2, S must live in Flat 1 of Floor 5.

Step 2: Determine L's floor
L lives on an even-numbered floor in Flat 1. The even floors are Floor 2 and Floor 4.

• Case A: L lives on Floor 4, Flat 1.
  If L lives on Floor 4, then N (who lives immediately below L's floor) must live on Floor 3. Since N lives west of Q, N is in Flat 1 of Floor 3, and Q is in Flat 2 of Floor 3.
  Since there is one floor between J and L, J must be on Floor 2.
  Also, since K and L live in different named flats, and L is in Flat 1, K must live in Flat 2. R lives in the same named flat as K, so R is also in Flat 2.
  Only one floor is between K and O, and K lives below O. This means O's floor number is 2 greater than K's floor number.
  If K is on Floor 1, O is on Floor 3 (but Floor 3 is occupied by N and Q, so this is impossible).
  If K is on Floor 2 (Flat 2), O must be on Floor 4 (Flat 2, since L is in Flat 1). M lives immediately below O but in a different named flat. Since O is in Flat 2 of Floor 4, M must be in Flat 1 of Floor 3. But N is already in Flat 1 of Floor 3. Thus, Case A is invalid.
• Case B: L lives on Floor 2, Flat 1.
  This must be the correct case. Let us place L at (Floor 2, Flat 1).

Step 3: Determine positions under Case B
Since L is at (Floor 2, Flat 1):

• N lives immediately below L, so N is on Floor 1. Since N is west of Q, N is at (Floor 1, Flat 1) and Q is at (Floor 1, Flat 2).
• There is one floor between J's floor and L's floor. Since L is on Floor 2, J must be on Floor 4.
• L is in Flat 1, which means K (living in a different named flat) must be in Flat 2. Since R lives in the same named flat as K, R is also in Flat 2.
• Only one floor is between K and O, and K lives below O. Since Floor 1, Flat 2 is occupied by Q, K must be on Floor 2 (Flat 2). This means O must be on Floor 4.
• Since J is on Floor 4 and O is on Floor 4, they occupy the two flats on Floor 4.
• M lives immediately below O (Floor 3), but not in the same named flat as O.
  • If O lives in Flat 1 of Floor 4, M would live in Flat 2 of Floor 3. This would leave no place for R in Flat 2 (since P, J, M, K, and Q would occupy Flat 2 on all floors).
  • Therefore, O must live in Flat 2 of Floor 4, which means J lives in Flat 1 of Floor 4.
  • Since O is in Flat 2 of Floor 4, M lives in Flat 1 of Floor 3.
• Finally, the only remaining position on Floor 3 is Flat 2, which must be occupied by R.

Summary Layout Table:

Thus, R lives in Flat 2 on the third floor.