Study the following information carefully and answer the questions given below.

Nine persons K, J, Y, R, D, L, X, P and S sit around a circular table but not necessarily in the same order. All of them are facing away from the centre of the table. K sits 3rd to the left of J. One person sits between K and X. Two persons sit between K and L. D sits immediately right of R and both of them are not adjacent to L. At least three persons sit between P and Y (both from left or right) . Y is not adjacent to S.

How many persons sit between the one who sits immediately right of Y and R when counted from left of R?

The correct option is None.

Step-by-step Explanation:

Let's arrange nine persons (K, J, Y, R, D, L, X, P, S) around a circular table facing away from the centre. Note that for persons facing away from the centre, clockwise corresponds to left and counter-clockwise corresponds to right (or vice-versa, depending on orientation; standard convention: facing away from centre means Right is counter-clockwise and Left is clockwise).

1. K sits 3rd to the left of J:
Let J be at position 1. Moving left (clockwise) around 9 positions:
Position 1: J
Position 2: _
Position 3: _
Position 4: K (3rd to the left of J)

2. One person sits between K and X:
X can be at position 2 or position 6.

3. Two persons sit between K and L:
L can be at position 1 (which is already occupied by J, so not possible) or position 7.
Thus, L is at position 7.

4. D sits immediately right of R and both are not adjacent to L (positions 6, 7, 8):
Positions adjacent to L are 6 and 8. So R and D cannot occupy 6, 7, or 8.
Available positions for (R, D) such that D is immediately right of R (counter-clockwise):
Since L is at 7, positions 6, 7, 8 are blocked for R and D.
Position 4 is K, 1 is J.
The open positions are among {2, 3, 5, 9}.
If R is at 3, D (immediately right of R) is at 2.
If X was at 2, then X would conflict. So X must be at 6!
Let's check: X at 6 (1 person between K at 4 and X at 6). This is valid!
So R is at position 3, and D is at position 2.

5. Remaining positions to fill for Y, P, S:
Positions occupied so far:
1: J
2: D
3: R
4: K
5: (P/Y/S)
6: X
7: L
8: (P/Y/S)
9: (P/Y/S)

6. At least three persons sit between P and Y (from both left and right):
In a circle of 9 people, for at least 3 persons to sit between two people from both sides, they must have either 3 people on one side and 4 on the other, or 4 on both (which total 9 with 2 people = 9).
Positions available for {P, Y, S} are 5, 8, 9.
If Y is at 5 and P is at 9 (or vice versa):
Between 5 and 9: positions {6, 7, 8} (3 persons) on one side, and {1, 2, 3, 4} (4 persons) on the other side. This satisfies "at least three persons sit between P and Y".
Then S takes position 8.

7. Y is not adjacent to S:
S is at position 8. Positions adjacent to 8 are 7 and 9.
So Y cannot be at position 9. Thus, Y is at position 5, and P is at position 9.
S is at position 8.

Complete Seating Arrangement (Clockwise from Position 1 to 9):
1: J
2: D
3: R
4: K
5: Y
6: X
7: L
8: S
9: P

Answering the question:
"How many persons sit between the one who sits immediately right of Y and R when counted from left of R?"
- Person immediately right of Y (facing away from centre, right is counter-clockwise/towards position 4): position 4, which is K.
- We need to count persons between K (position 4) and R (position 3) when counted from the left of R.
- Left of R (position 3) goes clockwise: position 4 (which is K).
- Therefore, starting from left of R (position 4), we immediately reach K. So there are None (0) persons between them.