Nine persons purchase different products one after the other. Either four or five persons purchase after K. Three persons purchase between K and L. M purchases just after L. Number of persons purchase before M is same as after N. O purchases between N and K. Q purchases just after P but before O. R purchases before S but after O.

Who among the following is second last person to purchase the product?

To determine the sequence in which the nine persons purchase products, we can break down the clues step-by-step to arrange them in order from 1st (first to purchase) to 9th (last to purchase).

Let the 9 positions be represented as 1, 2, 3, 4, 5, 6, 7, 8, and 9 from first to last.

Step 1: Locate the position of K.
The clue states: "Either four or five persons purchase after K."
- If 4 persons purchase after K, K is in the 5th position (since 9 - 4 = 5).
- If 5 persons purchase after K, K is in the 4th position (since 9 - 5 = 4).
Therefore, K is either in position 4 or position 5.

Step 2: Place L and M.
The clue states: "Three persons purchase between K and L."
- Case 1: K is in position 4.
L can be either in position 8 (since 4 + 3 + 1 = 8) or position 0 (not possible). So, L must be in position 8.
M purchases just after L, which means M is in position 9.
- Case 2: K is in position 5.
L can be in position 1 (since 5 - 3 - 1 = 1) or position 9 (since 5 + 3 + 1 = 9).
If L is in position 9, M (who purchases just after L) would have to be in position 10, which is impossible since there are only 9 people. Thus, L must be in position 1.
M purchases just after L, so M is in position 2.

Step 3: Analyze the relationship between M and N.
The clue states: "Number of persons purchase before M is same as after N."
- In Case 1 (M is in position 9):
There are 8 persons before M. Thus, there must be 8 persons after N, which means N must be in position 1.
- In Case 2 (M is in position 2):
There is 1 person before M. Thus, there must be 1 person after N, which means N must be in position 8.

Step 4: Place O.
The clue states: "O purchases between N and K."
- In Case 1: N is in 1, K is in 4. The positions between them are 2 and 3. So, O must be in position 2 or 3.
- In Case 2: K is in 5, N is in 8. The positions between them are 6 and 7. So, O must be in position 6 or 7.

Step 5: Place P and Q.
The clue states: "Q purchases just after P but before O." This means we have a consecutive block of "P, Q" that appears at some point before O.
- In Case 1:
If O is in position 2, there is only position 1 before O (which is occupied by N), so we cannot place the consecutive block "P, Q" before O.
If O is in position 3, the positions before O are 1 and 2. Since N is in 1, we cannot place the block "P, Q".
Thus, Case 1 is invalid.
- In Case 2:
We have L in 1, M in 2, K in 5, N in 8. O is in either 6 or 7.
The remaining empty positions are 3, 4, 6, 7, 9.
To place the consecutive block "P, Q" before O, the only available consecutive positions before position 6/7 are 3 and 4.
Therefore, P must be in position 3 and Q must be in position 4.
Since P and Q occupy 3 and 4, and they must purchase before O, O must be in one of the remaining slots after them. The positions 6 and 7 are open. O must be in position 6 or 7. Let's look at the next clue to determine the exact position of O.

Step 6: Place R and S.
The clue states: "R purchases before S but after O."
This means the order must be O followed by R followed by S (O ... R ... S).
If O is in position 7, the only positions remaining after O would be 8 (occupied by N) and 9. We would not have enough positions to place both R and S after O.
Therefore, O must be in position 6.
This leaves positions 7 and 9 empty.
Since R purchases before S, R must be in position 7 and S must be in position 9.

Final Arrangement:
1. L
2. M
3. P
4. Q
5. K
6. O
7. R
8. N
9. S

The second last person to purchase the product (position 8) is N.