Analyze the details provided below and answer the question that follows.

Eight individuals P, Q, R, T, U, V, X, and Y are seated in a single straight row, with some facing north and others facing south. No more than two adjacent individuals face the same direction.

Y is positioned at the extreme right end of the row and faces north. X sits to the immediate left of Y. P is seated at the extreme left end of the row, and exactly three individuals sit between P and U. V sits fourth to the right of Q, who faces north. R sits adjacent to both Q and T. X and V face in opposite directions. P and Q face the same direction, while T and U face opposite directions. R and T face the same direction, and V faces south.

The number of individuals sitting between R and Y is $\frac{4}{3}$ of the number of individuals sitting between ___ and ___.

Correct Answer: P, U

Step-by-step Explanation:

1. Determining the Seating Positions:

There are 8 individuals sitting in a row, which can be numbered 1 to 8 from left to right.

• Y is at the extreme right end (Position 8) and faces North.
• X sits to the immediate left of Y, so X is at Position 7.
• P is at the extreme left end (Position 1). Exactly three individuals sit between P and U, which places U at Position 5 (1 + 3 + 1 = 5).
• Q faces North, and V sits fourth to the right of Q. Since Q faces North, "right" means towards higher position numbers. Position of V = Position of Q + 4. The only available valid positions are Q at Position 2 and V at Position 6.
• R sits adjacent to both Q and T. Since Q is at Position 2, R must be at Position 3, and T must be at Position 4.

Thus, the positions from left to right (Positions 1 to 8) are:

Position 1: P
Position 2: Q
Position 3: R
Position 4: T
Position 5: U
Position 6: V
Position 7: X
Position 8: Y

2. Determining the Facing Directions:

• Y faces North and Q faces North.
• V faces South.
• X and V face opposite directions, so X faces North.
• P and Q face the same direction, so P faces North.
• P (Position 1) and Q (Position 2) both face North. Since no more than two adjacent individuals can face the same direction, R (Position 3) must face South.
• R and T face the same direction, so T (Position 4) faces South.
• T and U face opposite directions, so U (Position 5) faces North.

3. Calculating the Ratio and Identifying the Missing Pair:

The individuals sitting between R (Position 3) and Y (Position 8) are T, U, V, and X, which total 4 individuals.

According to the given statement:

$\text{Number of individuals between R and Y}=\frac{4}{3}\times \text{(Number of individuals between the missing pair)}$

Substituting the known value of 4:

$4=\frac{4}{3}\times \text{(Number of individuals between the missing pair)}$

$\text{Number of individuals between the missing pair}=3$

Now, let's check the number of individuals between P (Position 1) and U (Position 5):

The individuals sitting between P and U are Q, R, and T, which equals exactly 3 individuals.

Therefore, the missing pair is P, U.