Seven persons, K, L, M, N, O, P and Q, are sitting in a row facing towards the north. K and M are sitting together. O is at the east-end. P is between Q and M. Q is sitting in the middle. N is between O and L. K is sitting at the west-end. Who is sitting at the fifth position from the east?

Let's chart out the 7 positions from West (Left) to East (Right):
1(West),2,3,4(Middle),5,6,7(East)
Let's plug in the definite clues given in the problem:

"O is at the east-end." → Position 7 = O

"Q is sitting in the middle." → Position 4 = Q

"K is sitting at the west-end." → Position 1 = K

"N is between O and L." Since Position 7 is O, Position 6 must be N, and Position 5 must be L. Let's confirm: Position 5=L,Position 6=N,Position 7=O.

"P is between Q and M." Since Position 4 is Q, and Positions 5, 6, 7 are full, P must be at Position 3 and M must be at Position 2. Let's confirm: Position 2=M,Position 3=P,Position 4=Q.

"K and M are sitting together." Position 1 is K and Position 2 is M, which perfectly satisfies this condition.

The full arrangement from West to East is:

1
K
​

2
M
​

3
P
​

4
Q
​

5
L
​

6
N
​

7
O
​

The question asks for the person at the fifth position from the east:

1st from East = O (Pos 7)

2nd from East = N (Pos 6)

3rd from East = L (Pos 5)

4th from East = Q (Pos 4)

5th from East = P (Pos 3)

Thus, P is sitting at the fifth position from the east.