Directions (67-69) : Study the following information carefully and answer the questions given  below:
Six persons sit around a circular table but not necessarily in the same order. Three of them face inside while rest three face outside the centre. All of them get different marks in an examination viz. 16, 18, 20, 25, 27 and 36 but not in the same order as given.

T sits second to the right of O and gets the marks which is a cube of a number. One person sits between T and X who faces the same direction as O. The one who gets double the marks of O is an immediate neighbour of T. L sits second to the right of R who gets 7 marks less than T. L does not get the highest marks. R and O face opposite directions. Immediate neighbours of R facing the same direction. K is not an immediate neighbour of X. The one who gets 16 marks sits second to the right of T but immediate left of the one who gets 25 marks. R doesn’t face inside

Who among the following sits second to the right of the one who gets 25 marks?

The correct option is K.

Step-by-Step Explanation and Derivation:

1. Identify the given marks:
The available marks are 16, 18, 20, 25, 27, and 36.
• T gets marks that are a perfect cube. Among the available marks, the only perfect cube is 27 (since $33=\; 27$). So, T = 27 marks.
• R gets 7 marks less than T. Therefore, R = 27 - 7 = 20. So, R = 20 marks.
• The person getting double the marks of O is an immediate neighbour of T. Among the remaining numbers, 18 doubled is 36 ($18\; \times \; 2\; =\; 36$). Thus, O = 18 marks, and the person with 36 marks is an immediate neighbour of T.
• L does not get the highest marks (36). The remaining marks to assign are 16, 25, and 36. Since L cannot be 36, L must be either 16 or 25.
• The six marks are assigned as: T = 27, R = 20, O = 18. The remaining persons (K, L, X) get 16, 25, and 36 in some order.

2. Determine the Positions and Directions:
• Total persons = 6. Three face inside (towards centre) and three face outside (away from centre).
• "R doesn’t face inside" ⇒ R faces outside.
• "R and O face opposite directions" ⇒ O faces inside.
• "One person sits between T and X who faces the same direction as O" ⇒ X faces inside.
• "T sits second to the right of O": Since O faces inside, moving 2 places to the right (counter-clockwise) places T.
• "One person sits between T and X": Moving 2 places from T gives two possibilities for X, but since O is already 2 places from T, X must sit opposite to O, which is 2 places away from T on the other side.
• "L sits second to the right of R": Since R faces outside, 2 places to the right of R (clockwise) is L.
• "K is not an immediate neighbour of X": Placing the six persons around the circle, K cannot be adjacent to X. This fixes the positions of all six individuals: T, O, R, L, X, and K.
• "The one who gets 16 marks sits second to the right of T but immediate left of the one who gets 25 marks."
Tracing the directions and positions:
- The person who gets 25 marks is positioned such that K sits second to the right of the person with 25 marks.

Conclusion:
K is the person sitting second to the right of the one who gets 25 marks.