Directions (87-91) : Study the following information carefully and answer the questions given below.

Twelve persons sit on twelve seats arranged in a row but only some persons are known and all of them are facing towards the north direction. Y is the only neighbour of S. Three persons sit between S and O who sits immediately left of K. More than three persons sit between K and H. K sits 2nd to the left of P who sits exactly between K and U. The number of persons sit between P and B is multiple of 2. The prime number of persons sits between H and B.

The number of persons sit to the right of _____ is same as sit to the left of ____ respectively.

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Correct Answer: U, B

Step-by-Step Explanation:

Let us analyze the given conditions step-by-step to determine the exact arrangement of the 12 seats (numbered 1 to 12 from left to right), where all persons are facing North.

Step 1: Determine the positions of S, Y, O, and K.

1. "Y is the only neighbour of S."
This means S must sit at one of the extreme ends of the row so that it has only one adjacent seat.

• If S sits at the extreme left end (Seat 1), then Y must sit at Seat 2.
• If S sits at the extreme right end (Seat 12), then Y must sit at Seat 11.

2. "Three persons sit between S and O who sits immediately left of K."
• If S is at Seat 1, then 3 persons sit between S and O, placing O at Seat 5. Since O is immediately left of K, K must be at Seat 6.
• If S is at Seat 12, then 3 persons sit between S and O, placing O at Seat 8, which means K is at Seat 9.

Step 2: Determine the positions of P and U.

3. "K sits 2nd to the left of P who sits exactly between K and U."
• Since K is 2nd to the left of P, P must be 2 seats to the right of K.
• Since P is exactly in the middle of K and U, U must be 2 seats to the right of P.

Let's check our two possibilities:

• Case 1 (S at Seat 1):
K is at Seat 6.
P is at Seat 8 (2nd to the right of K).
U is at Seat 10 (2nd to the right of P).
This arrangement is valid.

• Case 2 (S at Seat 12):
K is at Seat 9.
P would be at Seat 11, but Seat 11 is already occupied by Y. Thus, Case 2 is invalid.

Therefore, Case 1 gives the correct positions:

Seat 1: S
Seat 2: Y
Seat 5: O
Seat 6: K
Seat 8: P
Seat 10: U

Step 3: Determine the position of B.

4. "The number of persons sit between P and B is a multiple of 2." and "The prime number of persons sits between H and B."
Since K is at Seat 6 and more than 3 persons sit between K and H, H must sit at Seat 11 or Seat 12.
Placing B at Seat 3 satisfies all conditions:
• Number of seats between P (Seat 8) and B (Seat 3) = $8-3-1=4$ (which is a multiple of 2).
• Number of seats between H (Seat 11) and B (Seat 3) = $11-3-1=7$ (which is a prime number).

Step 4: Answer the given question.

We need to find the pair where the number of persons sitting to the right of the first person is equal to the number of persons sitting to the left of the second person.

For U (Seat 10) and B (Seat 3):

• Number of persons to the right of U (Seat 10) = $12-10=2$ (Seats 11 and 12)

• Number of persons to the left of B (Seat 3) = $3-1=2$ (Seats 1 and 2)

Since both values are equal to 2, the correct pair filling the blanks is U, B.