Question

P, Q, R, S and T are standing in a row of \(33\) boys and all are facing North. S is \(15^{th}\) from the right end. P is to the right of Q and third to the left of R. S is to the right of T. What is the position of Q from the left end?

• A. \(12^{th}\)
• B. \(16^{th}\)
• C. \(18^{th}\)
• D. \(20^{th}\)

Hint:

To convert right-end position into left-end position, use total \(+1-\) right position.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a linear seating arrangement problem with 33 people facing North. We need to determine the absolute position of Q from the West end of the row based on the relative position rules given.

Step 2: Key Formula or Approach:
For any person in a row of total $N$ persons: \[ \text{Position from West (Left)} = N - (\text{Position from East (Right)}) + 1 \]

Step 3: Detailed Explanation:
Let us analyze the given rules step-by-step:
•

Step 1: Find the position of S from the West end
The total number of people in the row $N = 33$.
S is the 15th person from the East (Right) end.
Applying the formula: \[ \text{Position of S from West} = 33 - 15 + 1 = 19\text{th} \]
•

Step 2: Analyze the relative positions of Q, P, R, S, T
Since they are "standing together", they occupy 5 consecutive positions in the row. Let us arrange them:
• "P is to the right of Q": This means P is immediately to the right of Q $\implies \text{Order is } QP$.

• "P is third to the left of R": This means there are 2 people between P and R $\implies Q, P, \_, \_, R$.

• "S is to the right of T": Since they stand together, the remaining two spots between P and R must be filled by T and S in that order $\implies Q, P, T, S, R$.
This consecutive order is perfectly consistent with all criteria.
•

Step 3: Determine the position of Q
We know that S is at position 19 from the West end.
Since the consecutive order is $Q, P, T, S, R$:
• Position of S = 19

• Position of T = 18 (since T is immediately to the left of S)

• Position of P = 17 (since P is to the left of T)

• Position of Q = 16 (since Q is immediately to the left of P)
Thus, Q is 16th from the West end.

Step 4: Final Answer:
The position of Q from the West end is 16th, which corresponds to option (A).