Nine boys P, Q, R, S, T, U, V, W and X are sitting around a circular table…

Solution outline:

• Place Q at a reference position. Use right = clockwise and left = counter-clockwise.

• P is third to the right of Q → P is at position 3 (if Q is 0).

• U is fourth to the right of P → U is at position 7.

• X is fourth to the left of Q → X is at position 5.

• S is third to the left of X → S is at position 2.

• Remaining positions (1, 4, 6, 8) are for W, R, T, V. R is third to the right of W, and T is second to the left of V.

• A consistent assignment is: W at 1 → R at 4; V at 8 → T at 6.

Final seating (clockwise starting from Q at position 0):

• Q (position 0)

• W (position 1)

• S (position 2)

• P (position 3)

• R (position 4)

• X (position 5)

• T (position 6)

• U (position 7)

• V (position 8)

Evaluate each statement:

• I. "U and V are not the immediate neighbours."

  Analysis: U and V occupy adjacent positions (7 and 8), so the statement is incorrect.

• II. "V is the immediate neighbour of Q and U."

  Analysis: V is adjacent to positions 8 which neighbours U (7) and Q (0), so the statement is correct.

• III. "R is second to the right of T."

  Analysis: From T (position 6), second to the right is position 8 (V), not R (position 4). Statement is incorrect.

• IV. "W is third to the left of U."

  Analysis: Third to the left of U (position 7) is position 4 (R), not W (position 1). Statement is incorrect.

Conclusion: The statements that are not correct are I, III and IV.