Direction: Read the following information carefully and answer the questions given below. A certain number of people are sitting in a straight line facing north with equal distance between adjacent persons. Seven persons sits between T and P. U sits second to the right of W. Two persons sits between U and T. W sits second from the left end. S sits second to the left of Q. Q sits third to the left of P. V sits second to the left of X, who sits exactly between Q and U. P sits immediate left of R, who sits one of the extreme ends.
How many persons sits in the row?
Sixteen
Deducing Seating Positions Step-by-Step
This problem involves deciphering a linear seating arrangement puzzle. We need to find the total number of people based on a series of clues about their relative positions while facing north.
Step 1: Placing Individuals from End Clues
We start by placing individuals based on the most definitive clues:
- Clue: "P sits immediate left of R, who sits one of the extreme ends." Since everyone faces north, R is at the rightmost end. Let's assume the row has $N$ positions. R is at position $N$. P is immediately to R's left, so P is at position $N-1$.
- Clue: "Q sits third to the left of P." P is at position $N-1$. Q is 3 positions to the left of P, placing Q at position $(N-1) - 3 = N-4$.
- Clue: "Seven persons sits between T and P." P is at position $N-1$. If there are 7 people between T and P, then T must be $7 + 1 = 8$ positions to the left of P. So, T is at position $(N-1) - 8 = N-9$.
This establishes a partial structure towards the right end of the line: ... T ... Q ... P R.
Step 2: Determining Total Positions
Based on the clues, the arrangement from T to P spans 9 positions (T + 7 people + P). If R is at the end (position $N$), P is at $N-1$, and T is at $N-9$. This implies a minimum of $N-9$ positions are occupied from the start up to T. The sequence from T to R covers $(N-1) - (N-9) + 1 = 9 + 1 = 10$ positions. Given the options, let's test if $N=16$ works, as it is the correct answer.
- If $N=16$: R is at position 16.
- P is at position 15 (immediate left of R).
- Q is third to the left of P (position 15): $15 - 3 = 12$. Q is at position 12.
- T is 7 persons between T and P (position 15): T is at position $15 - 7 - 1 = 7$.
The arrangement skeleton for 16 positions is now established:
_ _ _ _ _ _ T _ _ _ Q _ _ P R (Positions 1 to 16).
Step 3: Placing Remaining Individuals
Now, let's place W, U, V, X, and S using the remaining clues:
- Clue: "W sits second from the left end." W is at position 2.
Arrangement:
_ W _ _ _ _ T _ _ _ Q _ _ P R - Clue: "U sits second to the right of W." W is at 2. U is at $2+2=4$.
Arrangement:
_ W _ U _ _ T _ _ _ Q _ _ P R - Clue: "X sits exactly between Q and U." U is at 4, Q is at 12. For X to be exactly between them, X's position must be the average of U's and Q's positions: $\frac{4 + 12}{2} = 8$. The order relative to U and Q must be U...X...Q.
- Clue: "V sits second to the left of X." X is at 8. V is at $8-2=6$.
Arrangement:
_ W _ U _ V T X _ _ Q _ _ P R - Clue: "S sits second to the left of Q." Q is at 12. S is at $12-2=10$.
Arrangement:
_ W _ U _ V T X _ S _ Q _ _ P R
Let's verify the clue "Two persons sits between U and T." U is at position 4, and T is at position 7. The positions between them are 5 and 6. This arrangement fits this clue.
Step 4: Finalizing the Arrangement and Count
The identified positions for the named individuals within the 16-person row are:
- W: Position 2
- U: Position 4
- V: Position 6
- T: Position 7
- X: Position 8
- S: Position 10
- Q: Position 12
- P: Position 15
- R: Position 16
The complete arrangement skeleton for 16 positions shows the placement of named individuals and the gaps:
Position: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Person: ? W ? U ? V T X ? S ? Q ? ? P R
There are 9 named individuals (T, P, U, W, S, Q, V, X, R) placed within these 16 positions. The remaining positions (1, 3, 5, 9, 11, 13, 14) must be occupied by other people to complete the row of 16.
Therefore, the total number of persons in the row is 16.
Similar Questions
Who faces W?
How many students are between W and R when counted from the left of W?
The same number of students are sitting between Y and ____ as that of between U and W.
Who is sitting to the immediate right of Q?
Who is sitting third to the left of V?
Four of the following five are alike in a certain way based on their seating position and thus form a group. Which of the following does not belong to the group?
Who is sitting opposite Q?
How many persons sits to the right of Q?
Who sits third to the right of U?
Which of the following statements is true regarding M?
Important Questions from Seating Arrangement
Five friends, Bhumika, Rashi, Shweta, Vibha and Arunima, are sitting in a row facing east. Bhumika is sitting between Vibha and Shweta. Rashi is second to the left of Shweta. Who is sitting at the south end?
O, P, Q, R, S, T and U are sitting in a row facing north. U is sitting to the immediate right of T. Q is sitting in between R and O. P, who is on the extreme right, is sitting to the immediate right of O. S is sitting to the immediate left of R. Who is sitting in the middle of the row ?
Six friends are sitting in a straight line. E is 4th from the right. E is between B and D. A is adjacent to B. D is adjacent to C. D is between E and C. F is adjacent to C. Who is sitting between F and D?
In hall there are seven children (including girls and boys) P, Q, R, S, T, U and V. They sit on three benches I, II and III. Such that at least two children on each bench and at least one girl on each bench. R who is a girl child, does not sit with P, T and S. U the boychild sit with only Q. P sits on the bench I with his best friends. V sits on the bench III. T is the brother of R. Who sits with R?
- Five people Palak, Karol, Risha, Saloni and Tishaare travelling in a car. The car has two seats in the front and three at the back. Rishais driving the car. Palak wants to sit at one of the window seats at the back of the car. Tisha wants to sit next to Palak. Karol hates Tisha and will not sit with Tisha. Who is sitting next to the driver ?
