In a row of certain number of students facing north, Anita’s position is 9th from the right end. There are exactly four students between Anita and Priya. Nisha is to the immediate right of Priya. If Nisha is at the most 7th from the left end of the row, what is the maximum possible number of students in the row?
19
For a person r-th from the right in a row of N, the position from the left is N − r + 1. Fix Anita first, place Priya on either side with four people between, then use Nisha's limit.
Step 1 — Anita is 9th from the right. With exactly four students between them, Priya is either 14th from the right (to Anita's left) or 4th from the right (to Anita's right).
Step 2 — Nisha is immediately to Priya's right, so Nisha is 13th or 3rd from the right.
Step 3 — Case 1: Nisha 13th from right. Her position from the left is \(N - 12 \le 7\), so \(N \le 19\).
Step 4 — Case 2: Nisha 3rd from right. Her position from the left is \(N - 2 \le 7\), so \(N \le 9\).
Step 5 — The largest possible row is therefore 19 students, with Nisha 7th from the left and 13th from the right.
18 is possible but not the largest, 9 is only the largest row in the second arrangement, and 10 is not possible at all, since the second arrangement allows at most 9 students and the first needs at least 14.
19 option is correct.
Similar Questions
In a row of students facing north, Rahul is 22nd from the left end and Diya is 16th from the right end. If there are exactly 8 people sitting between them, what are the maximum (x) and minimum (y) possible numbers of students in the row?
In a row of certain number of people facing north, Ravi’s position is 8th from the left end. There are exactly four people between Ravi and Meera. Sunita is to the immediate left of Meera. If Sunita is at the most 7th from one of the extreme ends of the row, what is the maximum possible value of the total number of people in the row?
Important Questions from Ordering and Ranking
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