Step 1: Determine the Position of S from the West End

The total number of persons in the row is 33.

S is the 15^th person from the East end.

The position of S from the West end is calculated as:

Position from West = Total Persons - Position from East + 1

The calculation is: \( S_{pos} = 33 - 15 + 1 = 19 \)

So, S is the 19^th person from the West end.

Step 2: Analyze Relative Positions

We are given the following relative positions:

• P is to the right of Q. This implies Q is somewhere to the left of P ( \( Q_{pos} < P_{pos} \) ).
• P is third to the left of R. This indicates two persons are between P and R, with R to the right of P. The sequence is P, X, Y, R. Mathematically, \( P_{pos} = R_{pos} - 3 \).
• S is to the right of T. This means T is somewhere to the left of S ( \( T_{pos} < S_{pos} \) ). Since \( S_{pos} = 19 \), we have \( T_{pos} < 19 \).

Step 3: Establish a Consistent Arrangement

We need to find the position of Q from the West end. Let's test the possibility that \( Q_{pos} = 16 \).

If \( Q_{pos} = 16 \), P must be to the right of Q, meaning \( P_{pos} > 16 \).

Let's consider the scenario where P is at the same position as S. Since \( S_{pos} = 19 \), we set \( P_{pos} = 19 \). This implies P and S refer to the same person.

Using the relation \( P_{pos} = R_{pos} - 3 \), if \( P_{pos} = 19 \), then \( R_{pos} = P_{pos} + 3 = 19 + 3 = 22 \).

Step 4: Verify the Arrangement

We verify if the arrangement \( Q=16, P=S=19, R=22 \) satisfies all given conditions:

• P (at position 19) is to the right of Q (at position 16)? Yes, as \( 19 > 16 \).
• P (at position 19) is third to the left of R (at position 22)? Yes. The positions relative to P are 19 (P), 20, 21, 22 (R). The difference is 3.
• S (at position 19) is to the right of T? This requires \( T_{pos} < 19 \), which is feasible (e.g., T could be at position 10).
• S (at position 19) is 15^th from the East end? Yes, calculation \( 33 - 19 + 1 = 15 \) confirms this.

As this arrangement is consistent with all conditions, the position of Q from the West end is 16^th.