Directions (96-100): Study the following information carefully and answer the questions given below.

Nine persons-K, L, M, N, O, P, Q, R and S purchase different products one after another but not necessarily in the same order. Three persons purchase products between K and M. R purchase product two persons before M. Two persons purchase product between R and O who purchase product before K. L purchase product just after K. Four persons purchase product between L and Q. The number of persons purchases products before K is same as the number of persons purchase products after Q. P purchase product before S but after M.

The number of persons purchases products before L is same as after____.

`. Let's prepare the response carefully. P

The correct answer is P.

Step-by-Step Logic and Derivation:

We are given that nine persons—K, L, M, N, O, P, Q, R, and S—purchase products one after another in positions numbered 1 to 9 from first to last.

1. Determining positions of K, L, and Q:

Let the position of K be k.

Since L purchases product just after K, position of L is:

$L=k+1$

The number of persons purchasing before K is $k-1$. Since the number of persons purchasing before K is the same as the number of persons purchasing after Q, the position of Q must be:

$Q=9-(k-1)=10-k$

Four persons purchase product between L and Q, which means the difference between their positions is 5:

$|L-Q|=5$

$\left|\right(k+1)-(10-k\left)\right|=5$

$|2k-9|=5$

Solving this gives two possibilities for k:

• If $2k-9=5$, then $k=7$. Then L = 8 and Q = 3. But 3 persons purchase between K and M, so M would be position 3 (which conflicts with Q = 3).

• If $2k-9=-5$, then $k=2$. This gives:

$K=2$
$L=3$
$Q=8$

2. Determining positions of M, R, and O:

Since 3 persons purchase between K (position 2) and M, position of M is:

$M=2+4=6$

R purchases two persons before M:

$R=6-2=4$

Two persons purchase between R and O, and O purchases before K (position 2):

$|R-O|=3\Rightarrow O=4-3=1$

3. Determining positions of P, S, and N:

P purchases before S but after M (position 6). The available remaining positions after position 6 are 7 and 9. Therefore:

$P=7$
$S=9$

The only remaining position 5 is filled by N:

$N=5$

Final Order (from 1 to 9):

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

Conclusion:

The number of persons purchasing products before L (position 3) is 2 (O and K).

The person who has 2 persons purchasing products after them is at position $9-2=7$, which is P (followed by Q and S).